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QUESTION: 1

Focal length of a convex lens of refractive index1.5 is 2 cm. Focal length of the lens whenimmersed in a liquid of refractive index of 1.25 will be [1988]

Solution:

QUESTION: 2

Ray optics is valid, when characteristicdimensions are [1989]

Solution:

Characteristic dimensions must be much

larger than the wavelength of light.

QUESTION: 3

A ray is incident at an angle of incidence i on one surface of a prism of small angle A and emerges normally from the opposite surface. If the refractive index of the material of prism is μ, the angle of incidence i is nearly equal to [1989]

Solution:

As refracted ray emerges normally from

oppostite surface, r_{2} = 0

QUESTION: 4

A beam of monochromatic light is refracted fromvacuum into a medium of refractive index 1.5,the wavelength of refracted light will be (1991]

Solution:

Here, c = velocity of light in medium and v =

velocity of light in vacuum;

m = refractive index of the medium.

Hence, wavelength in medium

(∴ μ > 1, given)

So, the required wavelength decreases.

ALTERNATIVELY,

c =vλ . On refraction, the frequency, v do

not change. When light is refracted from

vacuum to a medium, the velocity, c

decreases. Therefore, λ also decreases

QUESTION: 5

Green light of wavelength 5460 Å is incident onan air-glass interface. If the refractive index ofglass is 1.5, the wave length of light in glasswould be (c = 3 × 108 ms^{–1}) [1991]

Solution:

QUESTION: 6

There is a prism with refractive index equal to √2 and the refracting angle equal to 30°. One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is [1992]

Solution:

It is clear from the figure that the ray will

retrace the path when the refracted ray QR is

incident normally on the polished surface AC.

Thus, angle of refraction r = 30°

QUESTION: 7

Time taken by sunlight to pass through a window of thickness 4 mm whose refractive index is 3/2 is [1993]

Solution:

QUESTION: 8

A point source of light is placed 4 m below thesurface of water of refractive index 5/3. Theminimum diameter of a disc, which should beplaced over the source, on the surface of waterto cut off all light coming out of water is [1994]

Solution:

QUESTION: 9

Angle of deviation (δ) by a prism (refractive index = μ and supposing the angle of prism A to be small) can be given by [1994]

Solution:

When the angle of prism is small, δ = (μ – 1) A

QUESTION: 10

Focal length of a convex lens will be maximumfor [1994]

Solution:

For red light, focal length of lens is maximum

because f ∝ λ and λ is maximum for red

light.

QUESTION: 11

An achromatic combination of lenses is formedby joining [1995]

Solution:

If two or more lenses are combined together

in such a way that this combination

produces images of different colours at the

same point and of the same size, then this

property is called ‘achromatism’. Concave

and convex type of lenses are used for this

combination.

QUESTION: 12

The hypermetropia is a [1995]

Solution:

A person suffering from hyper metropia can

see objects beyond a particular point called

the near point. If the object lies at a point

nearer than this point, then image is not

formed at the retina. This is also known as

long-sight defect.

QUESTION: 13

If two mirrors are kept inclined at 60° to eachother and a body is placed at the middle, thentotal number of images formed is [1995]

Solution:

Angle between two mirrors (θ) = 60º. Number

of images formed by the inclined mirror

QUESTION: 14

A lens is placed between a source of light and a wall. It forms images of area A_{1} and A_{2} on the wall for its two different positions. The area of the source of light is [1995]

Solution:

Size of images = A_{1} and A_{2}. From the

displacement method, the area of the source

of light =

QUESTION: 15

A convex lens of focal length 80 cm and aconcave lens of focal length 50 cm are combinedtogether. What will be their resulting power? [1996]

Solution:

We know that

QUESTION: 16

If f_{V} and f_{R} are the focal lengths of a convex lensfor violet and red light respectively and F_{V} and F_{R} are the focal lengths of concave lens for violetand red light respectively, then we have [1996]

Solution:

According to Cauchy relation

Hence, red light having maximum wavelength

has maximum focal length.

∴ f_{v} < fr and also F_{v} > F_{r} as focal length is

negative for a concave lens.

QUESTION: 17

Light travels through a glass plate of thickness t and refractive index μ. If c is the speed of light in vacuum, the time taken by light to travel this thickness of glass is

Solution:

Total thickness = t; Refrative index = μ

Speed of light in Glass plate = c/μ

[where, t = thickness of glass plate]

QUESTION: 18

One face of a rectangular glass plate 6 cm thick issilvered. An object held 8 cm in front of the firstface forms an image 12 cm behind the silveredface. The refractive index of the glass is [1996]

Solution:

Thickness of glass plate (t) = 6 cm;

Distance of the object (u) = 8 cm.

And distance of the image (v) = 12 cm.

Let x = Apparent position of the silvered

surface in cm.

Since the image is formed due to relfection at

the silvered face and by the property of mirror

image

Distance of object from the mirror = Distance

of image from the mirror

or, x + 8 = 12 + 6 – x ⇒ x = 5 cm.

Therefore, refractive index of glass

QUESTION: 19

The focal length of converging lens is measuredfor violet, green and red colours. It is respectively f_{v}, f_{g}, f_{r}. We will get [1997]

Solution:

According to Cauchy relation

∴ Red light has wavelength greater than

violet light. Therefore focal length of lens

for red is greater than for violet. (f_{r} > f_{v})

QUESTION: 20

An astronomical telescope has a length of 44 cmand tenfold magnification. The focal length ofthe objective lens is [1997]

Solution:

Given : Length of astronomical telescope

(f_{0} + f_{e}) = 44 cm and magnification

From the given magnification, we find that f0

= 10fe. Therefore, 10f_{e} + f_{e} = 44 or 11f_{e} = 44 or

f_{e} = 4. And focal length of the objective

(f_{0}) = 44 – f_{e} = 44 – 4 = 40 cm.

QUESTION: 21

An electromagnetic radiation of frequency n, wavelength λ, travelling with velocity v in air enters in a glass slab of refractive index (ν). The frequency, wavelength and velocity of light in the glass slab will be respectively [1997]

Solution:

When electromagnetic wave enters in other

medium, frequency reamains unchanged

while wavelength and velocity become 1/μ times.

So, For e.m. wave entering from air to glass

slab (μ), frequency remains n,

QUESTION: 22

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On theother side of the lens, at what distance from thelens a convex mirror of radius of curvature 10 cmbe placed in order to have an upright image of theobject coincident with it? [1998]

Solution:

For the lens,

Coincidence is possible when the image is

formed at the centre of curvature of the

mirror. Only then the rays refracting through

the lens will fall normally on the convex mirror

and retrace their path to form the image at O.

So, the distance between lens and mirror

= 60 – 10 = 50 cm.

QUESTION: 23

Light enters at an angle of incidence in atransparent rod of refractive index n. For whatvalue of the refractive index of the material ofthe rod the light once entered into it will notleave it through its lateral face whatsoever bethe value of angle of incidence? [1998]

Solution:

Let a ray of light enter at A and the refracted

beam is AB. This is incident at an angle θ.

For no refraction at the lateral face, θ > C

or, sin θ > sin C But θ+ r =90°⇒θ= (90° – r)

QUESTION: 24

A plano-convex lens is made of material ofrefractive index 1.6. The radius of curvature ofthe curved surface is 60 cm. The focal length ofthe lens is [1999]

Solution:

QUESTION: 25

Wavelength of light of frequency 100 Hz [1999]

Solution:

QUESTION: 26

The refractive index of the material of the prismis √3 ; then the angle of minimum deviation ofthe prism is [1999]

Solution:

Angle of minimum deviation

QUESTION: 27

The radius of curvature of a thin plano-convexlens is 10 cm (of curved surface) and the refractiveindex is 1.5. If the plane surface is silvered, thenit behaves like a concave mirror of focal length [2000]

Solution:

The silvered plano convex lens behaves as a

concave mirror; whose focal length is given by

If plane surface is silvered

QUESTION: 28

A person is six feet tall. How tall must a verticalmirror be if he is able to see his entire length?

Solution:

To see his full image in a plane mirror a person

requires a mirror of at least half of his height.

QUESTION: 29

Rainbow is formed due to a combination of [2000]

Solution:

Rainbow is formed due to combination of

total internal reflection and dispersion.

QUESTION: 30

An air bubble in a glass slab (μ = 1.5) is 5 cmdeep when viewed from one face and 2 cm deepwhen viewed from the opposite face. Thethickness of the slab is [2000]

Solution:

∴ Thickness of the slab = R_{1} + R_{2}

= 7.5 + 3 = 10.5 cm

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