Ray Optics and Optical Instruments

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

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 109 m and its mean distance from the earth is 1.5 1011 m. What is the diameter of the sun's image on the paper ?

1. 6.5 10-5 m
2. 12.4 10-4 m
3. 9.2 10-4 m
4. 6.5 10-4 m

A small coin is resting on the bottom of a beaker filled with liquid. A ray of light from the coin travels up to the surface of the liquid and moves along its surface. How fast is the light travelling in the liquid? [figure]

1. 2.4 108 m/s
2. 3.0 108 m/s
3. 1.2 108 m/s
4. 1.8 108 m/s

The frequency of a light wave in a material is 2 1014 Hz and wavelength is 5000 A. The refractive index of material will be

1. 1.50
2. 3.00
3. 1.33
4. 1.40

A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again ?

1. 2 cm upward
2. 1 cm upward
3. 4.5 cm downward
4. 1 cm downward

A convex lens and a concave lens, each having same focal length of 25 cm, are put in contact to form a combination of lenses. The power in diopters of the combination is

1. zero
2. 25
3. 50
4. infinite.

The refractive index of the material of a prism is 2 and its refracting angle is 30 . One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is

1. 45
2. 60
3. 0
4. 30

A beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from

1. two points propagating in two different non-parallel directions
2. two points propagating in two different parallel directions
3. one point propagating in two different directions
4. one point propagating in the same directions

An equiconvex lens is cut into two halves along (i) XOX′ and (ii) YOY′ as shown in the figure. Let f, f', f'' be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively. Choose the correct statement from the following [figure]

1. f' = f, f'' = 2f
2. f' = 2f, f'' = f
3. f' = f, f'' = f
4. f' = 2f, f'' = 2f