Ray Optics and Optical Instruments

A lens having focal length f and aperture of diameter d forms an image of intensity I. The aperture of diameter d/2 in the central region of the lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

• f and 1/4

• 3f/4 and 1/2

• f and 3I/4

• f and 3I/4

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

• zero

• 30^o

• 45^o

• 45^o

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

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up to the surface of the liquid and moves along its surface (see figure).



How fast is the light travelling in the liquid?

• 1.8 x 10⁸ m/s

• 2.4 x 10⁸ m/s

• 3.0 x 10⁸ m/s

• 3.0 x 10⁸ m/s

The frequency  of a light wave in the material is 2 x 10 Hz and wavelength is 5000 A. the refractive index of material will be:

• 1.40

• 1.50

• 3.00

• 3.00

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 cm upward

• 4.5 cm downward

• 1 cm downward

• 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

• 25

• 50

• infinite

• infinite

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

• cot²θ = cot²θ₁+ cot²θ₂

• tan₂θ = tan²θ₁+ tan²θ₂

• cot²θ = cot²θ₁– cot²θ₂

• cot²θ = cot²θ₁– cot²θ₂

The ratio of resolving powers of an optical microscope for two wavelengths λ₁ = 4000 Å and λ₂ = 6000 Å is

• 8 : 27

• 9:4

• 3:2

• 3:2

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by

• y/2x

• y/x

• 2y/x

• 2y/x