Ray Optics and Optical Instruments

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance

1. 50.0 cm
2. 54.0 cm
3. 37.3 cm
4. 46.0 cm

The angle of incidence for a ray of light at a refracting surface of a prism is 45 . The angle of prism is 60 . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

1. 45 ; 2
2. 30 ; 1 2
3. 45 ; 1 2
4. 30 ; 2

Two identical glass ( g = 3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water ( w = 4/3). The focal length of the combination is

1. f/3
2. f
3. 4f/3
4. 3f/4

An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is

1. 8
2. 10
3. 12
4. 16

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be

1. convex, +2.25 diopter
2. concave, -0.25 diopter
3. concave, -0.2 diopter
4. convex, +0.15 diopter

A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. [figure] The prism will

1. not separate the three colours at all
2. separate the red colour part from the green and blue colours
3. separate the blue colour part from the red and green colours
4. separate all the three colours from one another

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is I. The magnification of the telescope is

1. L+IL-I
2. LI
3. LI+1
4. LI-1

Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is

1. -50 cm
2. 50 cm
3. -20 cm
4. -25 cm

The refracting angle of a prism is A, and refractive index of the material of the prism is (A/2). The angle of minimum deviation is

1. 90 - A
2. 180 + 2A
3. 180 - 3A
4. 180 - 2A

If the focal length of objective lens is increased then magnifying power of

1. microscope will increase but that of telescope decrease.
2. microscope and telescope both will increase.
3. microscope and telescope both will decrease.
4. microscope will decrease but that of telescope will increase.

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index , of the prism is

1. 2sinA
2. 2cosA
3. 12cosA
4. tanA

A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices 1 and 2 and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

1. R( 1- 2)
2. 2R( 2- 1)
3. R2( 1+ 2)
4. R2( 1- 2)

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be

1. 1.67 cm
2. 1.5 cm
3. 5 cm
4. 2.5 cm

The reddish appearance of the sun at sunrise and sunset is due to

1. the scattering of light
2. the polarisation of light
3. the colour of the sun
4. the colour of the sky

Two plane mirrors are inclined at 70 . A ray incident on one mirror at angle , after reflection falls on second mirror and is reflected from there parallel to first mirror. The value of is

1. 45
2. 30
3. 55
4. 50

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

1. lies between 2 and 1
2. lies between 2 and 2
3. is less than 1
4. is greater than 2

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is

1. 10 cm
2. 15 cm
3. 2.5 cm
4. 5 cm

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index

1. equal to that of glass
2. less than one
3. greater than that of glass
4. less than that of glass

A ray of light is incident at an angle of incidence i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is , the angle of incidence i, is nearly equal to

1. A
2. A2
3. A
4. A2

A concave mirror of focal length f1 is placed at a distance of d from a convex lens of focal length f2. A beam of light coming from infinity and falling on this convex lens – concave mirror combination returns to infinity. The distance d must equal

1. f1 + f2
2. -f1 + f2
3. 2f1 + f2
4. -2f1 + f2

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal length of lenses are

1. 10 cm, 10 cm
2. 15 cm, 5 cm
3. 18 cm, 2 cm
4. 11 cm, 9 cm

A thin prism of angle 15 made of glass of refractive index 1 = 1.5 is combined with another prism of glass of refractive index 2 = 1.75. The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

1. 5
2. 7
3. 10
4. 12

A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is

1. 5 cm
2. -10 cm
3. 20 cm
4. -30 cm

Which of the following is not due to total internal reflection ?

1. Working of optical fibre
2. Difference between apparent and real depth of a pond
3. Mirage on hot summer days
4. Brilliance of diamond

A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the following options best describes the image formed of an object of height 2 cm placed 30 cm from the lens ?

1. Virtual, upright, height = 1 cm
2. Virtual, upright, height = 0.5 cm
3. Real, inverted, height = 4 cm
4. Real, inverted, height = 1 cm

The speed of light in media M1 and M2 are 1.5 108 m/s and 2.0 108 m/s respectively. A ray of light enters from medium M1 to M2 at an incidence angle i. If the ray suffers total internal reflection, the value of i is

1. Equal to -1 ( 23 )
2. Equal to or less than -1 ( 35 )
3. Equal to or greater than -1 ( 34 )
4. Less than -1 ( 23 )

A ray of light is incident on a 60 prism at the minimum deviation position. The angle of refraction at the first face (i.e., incident face) of the prism is

1. zero
2. 30
3. 45
4. 60

A ray of light travelling in a transparent medium of refractive index , falls on a surface separating the medium from air at an angle of incidence of 45 . For which of the following value of the ray can undergo total internal reflection?

1. = 1.33
2. = 1.40
3. = 1.50
4. = 1.25

A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

1. f and I4
2. 3f4 and I2
3. f and 3I4
4. f2 and I2

Two thin lenses of focal lengths f1 and f2 are in contact and coaxial. The power of the combination is

1. f1 + f22
2. f1 + f2f1 f2
3. f1f2
4. f2f1