Physical Science Classes VI-X for School Assistants and TET Paper 2A · Chapter 5

Light: Reflection, Refraction, Lenses, Eye, Prism, Dispersion and Scattering

What to remember

Light travels in straight lines at about 3 x 10⁸ m/s in vacuum. Reflection obeys two laws; refraction obeys Snell's law (n₁ sin i = n₂ sin r). Mirror formula: 1/v + 1/u = 1/f; lens formula: 1/v − 1/u = 1/f; power P = 1/f in dioptre.
Concave mirrors and convex lenses are converging; convex mirrors and concave lenses are diverging. Myopia is corrected with a concave lens and hypermetropia with a convex lens.
White light splits into VIBGYOR in a prism (dispersion). Blue sky, red sunset and the Tyndall effect are due to scattering.

Reflection and plane mirrors

Laws of reflection: (1) the angle of incidence equals the angle of reflection (∠i = ∠r); (2) the incident ray, the reflected ray and the normal at the point of incidence lie in the same plane. Angles are measured from the normal.

Image in a plane mirror: virtual, erect, same size as the object, as far behind the mirror as the object is in front, and laterally inverted. If the mirror turns through an angle θ, the reflected ray turns through 2θ. Two mirrors at angle θ form about (360/θ) − 1 images. A person 1 m from the mirror is 2 m from the image.

Spherical mirrors

A concave mirror curves inward (converging); a convex mirror curves outward (diverging). Terms: pole (P), centre of curvature (C), radius of curvature (R), principal axis, principal focus (F). Focal length f = R/2.

New Cartesian sign convention: distances are measured from the pole; distances along the direction of incident light are positive; against it, negative. For a real object the object distance u is negative. A concave mirror has negative f; a convex mirror has positive f.

Mirror formula: 1/v + 1/u = 1/f
Magnification: m = h′/h = −v/u. Negative m means a real, inverted image; positive m means a virtual, erect image.

Object position (concave mirror)	Image
At infinity	At F, real, inverted, highly diminished
Beyond C	Between F and C, real, inverted, diminished
At C	At C, real, inverted, same size
Between C and F	Beyond C, real, inverted, enlarged
At F	At infinity, real, inverted, highly enlarged
Between F and P	Behind the mirror, virtual, erect, enlarged

A convex mirror always gives a virtual, erect, diminished image behind the mirror, with a wide field of view.

Uses: concave mirror in shaving mirrors, dentist's mirror, torch and car headlights, solar cookers; convex mirror as a rear-view mirror in vehicles.

Worked example: a concave mirror has f = −10 cm. An object is placed 30 cm in front (u = −30). 1/v = 1/f − 1/u = −1/10 + 1/30 = −2/30, so v = −15 cm (real image, 15 cm in front); m = −v/u = −(−15)/(−30) = −0.5 (inverted, half size).

Refraction and refractive index

Refraction is the bending of light when it passes from one transparent medium to another because its speed changes. In going from a rarer to a denser medium, light bends towards the normal; from denser to rarer, away from the normal. Light falling along the normal does not bend.

Laws of refraction: (1) the incident ray, refracted ray and normal are in the same plane; (2) Snell's law: sin i / sin r = constant (n for the second medium relative to the first).

Absolute refractive index n = c / v (speed in vacuum / speed in the medium). It has no unit. Approximate values: air about 1.0003; water about 1.33; glass about 1.5; diamond about 2.4 (highest in common use). Optically denser means higher n, not higher mass density.

Examples of refraction: a pencil appears bent in water; a pond appears shallower than it is; a coin in a cup becomes visible when water is added; stars twinkle; the Sun is seen slightly before actual sunrise.

Total internal reflection (TIR): when light goes from a denser to a rarer medium at an angle of incidence more than the critical angle, it is wholly reflected. Conditions: denser to rarer medium, and angle greater than the critical angle. Uses and examples: optical fibres (communication and endoscopy), sparkle of diamond (small critical angle), mirage, prism periscope and binoculars.

Lenses

A convex lens is thicker at the centre and converging; a concave lens is thinner at the centre and diverging. Terms: optical centre, principal axis, principal focus, focal length.

Lens formula: 1/v − 1/u = 1/f
Magnification: m = v/u
Power: P = 1/f (f in metres); unit dioptre (D). Convex lens: positive power; concave lens: negative power. A lens of f = +50 cm has P = +2 D. Powers of lenses in contact add: P = P₁ + P₂.

Object position (convex lens)	Image
At infinity	At F, real, inverted, highly diminished
Beyond 2F	Between F and 2F, real, inverted, diminished
At 2F	At 2F, real, inverted, same size
Between F and 2F	Beyond 2F, real, inverted, enlarged
At F	At infinity, real, inverted, highly enlarged
Between F and O	Same side, virtual, erect, enlarged (magnifying glass)

A concave lens always gives a virtual, erect, diminished image on the same side as the object.

Worked example: object 20 cm from a convex lens of f = 10 cm: u = −20; 1/v = 1/10 − 1/20 = 1/20, so v = +20 cm; m = v/u = −1 (real, inverted, same size).

Uses: convex lens in magnifying glass, camera, projector, microscope, telescope and spectacles for hypermetropia; concave lens in spectacles for myopia.

The human eye

Light enters through the cornea, passes the pupil (opening controlled by the iris) and the eye lens, and forms a real, inverted image on the retina, which has rods (dim light) and cones (colour). The optic nerve carries the signal to the brain. The ciliary muscles change the focal length of the lens (accommodation). Normal near point is 25 cm; far point is infinity. The eye keeps an image for about 1/16 second (persistence of vision), which is the basis of cinema.

Defect	Cause	Correction
Myopia (short sight)	Image forms in front of the retina; distant objects blurred	Concave lens
Hypermetropia (long sight)	Image forms behind the retina; near objects blurred	Convex lens
Presbyopia	Weak ciliary muscles in old age	Bifocal lens
Cataract	Lens becomes cloudy	Surgery
Astigmatism	Uneven curvature of the cornea	Cylindrical lens

Vitamin A deficiency causes night blindness. Colour blindness is a defect of the cones.

Prism, dispersion and the spectrum

A prism bends light towards its base. Dispersion is the splitting of white light into its seven colours: violet, indigo, blue, green, yellow, orange, red (VIBGYOR). Each colour has a different speed in glass: red travels fastest and bends least; violet bends most. Newton showed that a second inverted prism recombines the colours into white light. The primary colours of light are red, green and blue.

A rainbow is formed by refraction, dispersion and internal reflection of sunlight in raindrops; it is seen when the Sun is behind the observer and rain is in front.

Scattering of light

Scattering is the spreading of light by particles in its path. Short-wavelength light (blue) is scattered much more than long-wavelength light (red) by particles smaller than the wavelength (Rayleigh scattering, proportional to 1/λ⁴).

Blue sky: blue light is scattered most by air molecules. Without an atmosphere the sky would look dark, as seen by astronauts.
Red Sun at sunrise and sunset: light travels a longer path through the air, the blue is scattered away, and the red reaches the eye.
Danger signals are red because red is scattered least and can be seen from far away.
Tyndall effect: scattering of light by colloidal particles, as when sunlight enters a forest through mist or a beam is seen in a dusty room.
Clouds look white because the large water droplets scatter all colours.

Exam traps

Real images are inverted and can be placed on a screen; virtual images are erect and cannot.
A plane mirror image is laterally inverted, not upside down.
A convex lens is converging; a convex mirror is diverging.
Power of a lens is in dioptre and uses f in metres, not centimetres.
Myopia uses a concave lens; hypermetropia uses a convex lens.
Red light bends least in a prism; violet bends most.
Sky is blue due to scattering, not because of reflection from the sea.
The image on the retina is inverted; the brain turns it upright.

One-liners

1. Speed of light in vacuum is about 3 x 10⁸ m/s.
2. f = R/2 for a spherical mirror.
3. A rear-view mirror is a convex mirror.
4. n = c / v.
5. Unit of lens power is the dioptre.
6. Myopia is corrected by a concave lens.
7. Hypermetropia is corrected by a convex lens.
8. Violet bends the most in a prism.
9. The primary colours of light are red, green and blue.
10. Normal near point of the eye is 25 cm.
11. The danger signal is red.
12. Optical fibres work on total internal reflection.

Practice questions

The image formed by a plane mirror is
1. virtual and enlarged
2. real and inverted
3. real and diminished
4. virtual, erect and of the same size
Answer
D. virtual, erect and of the same size
A plane mirror gives a virtual, erect, same-size, laterally inverted image.
The mirror used as a rear-view mirror in vehicles is
1. plane
2. concave
3. cylindrical
4. convex
Answer
D. convex
A convex mirror gives an erect, diminished image with a wide field of view.
A dentist uses which type of mirror to see an enlarged image of a tooth?
1. Concave mirror
2. Convex mirror
3. Plane mirror
4. Cylindrical mirror
Answer
A. Concave mirror
A concave mirror with the object between P and F gives an enlarged, erect image.
The SI unit of power of a lens is
1. watt
2. dioptre
3. metre
4. candela
Answer
B. dioptre
P = 1/f with f in metres, measured in dioptre.
A person with myopia is advised to use
1. a concave lens
2. a convex lens
3. a bifocal lens only
4. a plane glass
Answer
A. a concave lens
A concave lens diverges the rays and moves the image back onto the retina.
Hypermetropia is corrected with
1. a cylindrical lens
2. a convex lens
3. a prism
4. a concave lens
Answer
B. a convex lens
A convex lens converges the rays so the image falls on the retina.
When white light passes through a glass prism, the colour that bends the least is
1. violet
2. green
3. red
4. blue
Answer
C. red
Red has the longest wavelength, the highest speed in glass and the least deviation.
The sky appears blue because of
1. refraction by clouds
2. absorption of red light by ozone
3. reflection from the sea
4. scattering of blue light by air molecules
Answer
D. scattering of blue light by air molecules
Short wavelengths are scattered much more strongly.
The Sun looks red at sunrise and sunset because
1. red light is scattered most
2. blue light is scattered away over the long path in air
3. the Sun is nearer to Earth
4. the Sun becomes cooler
Answer
B. blue light is scattered away over the long path in air
Only the least scattered red and orange reach the eye.
Danger signals are red in colour because red light
1. is scattered the least
2. is the brightest colour
3. has the shortest wavelength
4. is scattered the most
Answer
A. is scattered the least
It travels the farthest through fog and dust.
Among common materials, the highest refractive index is that of
1. water
2. glass
3. air
4. diamond
Answer
D. diamond
Diamond is about 2.4, glass about 1.5, water about 1.33.
Optical fibres work on the principle of
1. scattering
2. dispersion
3. total internal reflection
4. diffraction
Answer
C. total internal reflection
Light is repeatedly totally reflected inside the thin glass fibre.
The least distance of distinct vision for a normal eye is about
1. 50 cm
2. 10 cm
3. 1 m
4. 25 cm
Answer
D. 25 cm
The near point of a normal eye is 25 cm.
When light passes from air into glass, it
1. does not bend
2. bends away from the normal
3. bends towards the normal
4. is totally reflected
Answer
C. bends towards the normal
Light bends towards the normal on entering a denser medium.
The cells of the retina that detect colour are the
1. rods
2. cones
3. iris cells
4. ciliary cells
Answer
B. cones
Cones work in bright light and give colour vision; rods work in dim light.
The deficiency of which vitamin causes night blindness?
1. Vitamin A
2. Vitamin B
3. Vitamin D
4. Vitamin C
Answer
A. Vitamin A
Vitamin A is needed for the pigment in rods.
Which of the following can be obtained on a screen?
1. A real image
2. A mirror image of a plane mirror
3. An image in a convex mirror
4. A virtual image
Answer
A. A real image
Only real images are formed by actual meeting of rays.
The radius of curvature of a concave mirror is 30 cm. Its focal length is
1. 7.5 cm
2. 15 cm
3. 60 cm
4. 30 cm
Answer
B. 15 cm
f = R/2 = 15 cm.
A convex lens has a focal length of 50 cm. Its power is
1. -2 D
2. +0.5 D
3. +50 D
4. +2 D
Answer
D. +2 D
P = 1/f = 1/0.5 = +2 D.
Which of the statements is/are correct? 1. Light needs a material medium to travel. 2. The speed of light in vacuum is about 3 x 10^8 m/s.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Light travels through vacuum, so no medium is needed.
A concave lens has a focal length of 25 cm. Its power is
1. +4 D
2. -0.25 D
3. -4 D
4. -25 D
Answer
C. -4 D
P = 1/(-0.25 m) = -4 D.
Two thin lenses of powers +2 D and -0.5 D are placed in contact. The combined power is
1. +1.5 D
2. -1.5 D
3. +2.5 D
4. +4 D
Answer
A. +1.5 D
Powers add: 2 + (-0.5) = 1.5 D.
An object is 20 cm in front of a convex lens of focal length 10 cm. The image is formed at
1. infinity
2. 10 cm on the other side
3. 20 cm on the other side
4. 30 cm on the same side
Answer
C. 20 cm on the other side
1/v = 1/10 - 1/20 = 1/20, so v = 20 cm; the image is real, inverted and same size.
An object is 30 cm in front of a concave mirror of focal length 10 cm. The image distance is
1. 7.5 cm in front of the mirror
2. 15 cm behind the mirror
3. 30 cm in front of the mirror
4. 15 cm in front of the mirror
Answer
D. 15 cm in front of the mirror
1/v = 1/f - 1/u = -1/10 + 1/30 = -1/15, so v = -15 cm (real image).
The speed of light in a medium of refractive index 2 is (c = 3 x 10^8 m/s)
1. 6 x 10^8 m/s
2. 1.5 x 10^8 m/s
3. 3 x 10^8 m/s
4. 2 x 10^8 m/s
Answer
B. 1.5 x 10^8 m/s
v = c/n = 3 x 10^8 / 2 = 1.5 x 10^8 m/s.
A plane mirror is rotated through 10 degrees with the incident ray fixed. The reflected ray turns through
1. 40 degrees
2. 10 degrees
3. 20 degrees
4. 5 degrees
Answer
C. 20 degrees
The reflected ray turns through twice the angle of rotation of the mirror.
A girl stands 2 m in front of a plane mirror. The distance between her and her image is
1. 8 m
2. 1 m
3. 2 m
4. 4 m
Answer
D. 4 m
The image is 2 m behind the mirror, so the separation is 2 + 2 = 4 m.
An object is 15 cm in front of a convex lens of focal length 10 cm. The magnification is
1. +2
2. -1/2
3. +1/2
4. -2
Answer
A. +2
1/v = 1/10 - 1/15 = 1/30, so v = 30 cm; m = v/u = 30/(-15) = -2 (real and inverted, twice the size).
The refractive index of a medium is found to be 1.5 when sin i = 0.6. The value of sin r is
1. 0.4
2. 1.5
3. 0.3
4. 0.9
Answer
A. 0.4
n = sin i / sin r, so sin r = 0.6/1.5 = 0.4.
The critical angle of a medium of refractive index 2 (with respect to air) is
1. 60 degrees
2. 45 degrees
3. 30 degrees
4. 90 degrees
Answer
C. 30 degrees
sin C = 1/n = 1/2, so C = 30 degrees.
The focal length of a convex mirror of radius of curvature 40 cm is
1. -20 cm
2. -80 cm
3. +40 cm
4. +20 cm
Answer
D. +20 cm
f = R/2 = 20 cm, positive for a convex mirror in the Cartesian convention.
A pencil dipped in water appears bent because of
1. reflection of light
2. refraction of light
3. dispersion
4. scattering
Answer
B. refraction of light
Light bends as its speed changes at the water-air boundary.
A rainbow is formed due to
1. only reflection from clouds
2. diffraction in air
3. scattering by dust
4. refraction, dispersion and internal reflection in raindrops
Answer
D. refraction, dispersion and internal reflection in raindrops
Each raindrop acts like a small prism.
A spectacle lens for a person who cannot see distant objects clearly should have
1. negative power
2. positive power
3. zero power
4. power in watts
Answer
A. negative power
Myopia needs a diverging (concave) lens, of negative power.
The image formed on the retina is
1. real and erect
2. real and inverted
3. virtual and erect
4. virtual and inverted
Answer
B. real and inverted
The brain interprets it as upright.
Clouds appear white because
1. droplets absorb red light
2. large droplets scatter all colours nearly equally
3. they reflect blue light only
4. they emit white light
Answer
B. large droplets scatter all colours nearly equally
Large particles do not favour short wavelengths.
A teacher shows a thin beam of sunlight in a dusty room to explain
1. total internal reflection
2. dispersion
3. the Tyndall effect
4. polarisation
Answer
C. the Tyndall effect
Dust particles scatter the light so the path becomes visible.
Which of the statements is/are correct? 1. A convex mirror always forms a virtual, erect and diminished image. 2. A concave lens always forms a real image.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
A concave lens always gives a virtual, erect, diminished image.
Which of the statements is/are correct? 1. Violet light bends more than red light in a prism. 2. Red light has a shorter wavelength than blue light.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Red has the longer wavelength.
Which of the statements is/are correct? 1. Total internal reflection occurs when light goes from a denser to a rarer medium. 2. It occurs at any angle of incidence.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
The angle of incidence must exceed the critical angle.
Which of the statements is/are correct? 1. Optical density and mass density of a medium are the same. 2. Light travels slower in a medium of higher refractive index.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Optical density is not the same as mass density; v = c/n.
Which of the statements is/are correct? 1. Presbyopia is caused by weakening of ciliary muscles. 2. Cataract is corrected using a concave lens.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
Cataract is treated by surgery.
Which of the pairs is correctly matched?
1. Cataract - bifocal lens
2. Myopia - convex lens
3. Astigmatism - cylindrical lens
4. Hypermetropia - concave lens
Answer
C. Astigmatism - cylindrical lens
Myopia needs concave, hypermetropia convex; astigmatism needs cylindrical.
Which of the statements is/are correct? 1. Stars twinkle because of atmospheric refraction. 2. Danger signals are red because red light is scattered the least.
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
Both are standard facts.

Page 1 of 1

Chapter quiz · 10 questions

0/10 answered

On what you just read, from the live question bank. 🔒 Answers and solutions are shown to registered students (free).
अध्याय पढ़ने के बाद अभ्यास करें।

1.________is not an example of refraction of light.
2.Light travels from air into water with an index of refraction of 1.33. The light ray will:
3.Which of the following is NOT due to refraction of light?
4.Which of the following is NOT an example of refraction of light?
5.Which set of sign conventions is followed while dealing with reflection of light by spherical mirrors?
6.When a parallel beam of light passes through a convex lens, after refraction it:
7.When light is incident on a polished surface, __________ reflection takes place.
8.A beam of light parallel to the ________ of a concave mirror will pass through the principal focus after reflection.
9.For a ray of light undergoing refraction through a triangular glass prism, which of the following statements is/are always correct? (a) Angle of incidence is the angle between the incident ray and normal at the point of incidence. (b) Angle of incidence is equal to angle of emergence. (c) Angle of deviation is the angle between incident ray and emergent ray.
10.For a given colour and given pair of media, and light is going from rarer to denser media, the ratio of sine of the angle of incidence to the sine of angle of refraction is:

10 left. You can check any time.