ray optics and optical instruments

For a given lens, the magnification was found to be
twice as large as when the object was 0.15 m
distant from it as when the distance was 0.2 m. The
focal length of the lens is

• 1.5 m

• 0.20 m

• 0.10 m

• 0.05 m

The two lenses of an achromatic doublet should have

• equal powers

• equal dispersive powers

• equal ratio of their power and dispersive power

• sum of the product of their powers and dispersive power equal to zero

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm.  On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it

• 30 cm

• 60 cm

• 50 cm

• 12 cm

A point source of light is placed 4 m below the surface of water of refractive index 5/3. The minimum diameter of a disc which should be placed over the source on the surface of water to cut-off all light coming out of water is

• 6 m

• 3 m

• 4 m

• 2 m

To get three images of a single object, we should have two plane mirrors at an angle of

• 60^o

• 90^o

• 120^o

• 30^o

A vessel of depth t is half filled with a liquid having refractive index n₁ and the other half is filled with water of having refractive index n₂. The apparent depth of the vessel as viewed from top is

• $\frac{2\mathrm{t} \left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}{{\mathrm{n}}_1 {\mathrm{n}}_2}$

• $\frac{\mathrm{t} {\mathrm{n}}_1 {\mathrm{n}}_2}{\left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}$

• $\frac{\mathrm{t} \left({\mathrm{n}}_1 + {\mathrm{n}}_2\right)}{2 {\mathrm{n}}_1 {\mathrm{n}}_2}$

• $\frac{{\mathrm{n}}_1 {\mathrm{n}}_2}{\left( {\mathrm{n}}_1 + {\mathrm{n}}_2 \right)}$

A fish rising vertically to the surface of water in a lake uniformly at the rate of 2 m/s observes a kingfisher diving vertically towards the water at a rate of 10 m/s. If refractive index of water n = $\frac{4}{3}$ what will be the actual velocity of the kingfisher

• 10 m/s

• 8 m/s

• 6 m/s

• 9 m/s

A square wire of side 2.0 cm is placed 20 cm in front of a concave mirror of focal length 10 cm with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of wire is

• 7.5 cm²

• 6 cm²

• 2 cm²

• 4 cm²

A quarter cylinder of radius R and refractive index 1.5 is placed on a table. A point object P is kept at a distance ofmR from it as shown in figure. For what value of m for which a ray from P will emerge parallel to the table?

• $\frac{2}{3}$

• $\frac{3}{2}$

• $\frac{4}{3}$

• $\frac{3}{4}$

Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 A^o. When the slit is illuminated by light of another wavelength, then the angular width decreases by 30%. The same decrease in angular width of central maximum is obtained when the original apparatus is immersed in a liquid. The refractive index of the liquid will be

• 1.25

• 1.42

• 1.67

• 1.5