A plano-convex lens fits exactly into a plane-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices ${\mathrm{\mu }}_1 \mathrm{and} {\mathrm{\mu }}_2$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

1. $\frac{\mathrm{R}}{2({\mathrm{\mu }}_1+{\mathrm{\mu }}_2)}$

2. $\frac{\mathrm{R}}{2({\mathrm{\mu }}_1-{\mathrm{\mu }}_2)}$

3. $\frac{\mathrm{R}}{({\mathrm{\mu }}_1-{\mathrm{\mu }}_2)}$

4. $\frac{2\mathrm{R}}{({\mathrm{\mu }}_2-{\mathrm{\mu }}_1)}$

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

1. 5cm

2. 2.5cm

3. 1.67cm

4. 1.5cm

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

1. 10cm, 10cm

2. 15cm, 5cm

3. 18cm, 2cm

4. 11cm, 9cm

A ray of light 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 $\mathrm{\mu }$, the angle of the incidence i, is nearly equal to

1. $\frac{\mathrm{A}}{\mathrm{\mu }}$

2. $\frac{\mathrm{A}}{2\mathrm{\mu }}$

3. $\mathrm{\mu A}$

4. $\frac{\mathrm{\mu A}}{2}$

A concave mirror of focal length ${\mathrm{f}}_1$ is placed at a distance of d from a convex lens of focal length ${\mathrm{f}}_2$. 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. $2{\mathrm{f}}_1+{\mathrm{f}}_2$

2. $-2{\mathrm{f}}_1+{\mathrm{f}}_2$

3. ${\mathrm{f}}_1+{\mathrm{f}}_2$

4. $-{\mathrm{f}}_1+{\mathrm{f}}_2$

A converging beam of rays is incident on a diverging lens. Having passed through the lens ,the rays intersect at a point 15cm 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. 5cm

2. -10cm

3. 20cm

4. -30cm

A thin prism of angle $15°$ made of glass of refractive index ${\mathrm{\mu }}_1=1.5$ is combined with another prism of glass of refractive index ${\mathrm{\mu }}_2=1.75$. 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 telescope has an objective lens of 10cm diameter and is situated at a distance of 1 km from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 $\stackrel{°}{\mathrm{A}}$, is of the order of

1. 5m

2. 5 mm

3. 5 cm

4. 0.5 m

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

1. f'=f, f''=2f

2. f'=2f, f''=f

3. f'=f, f''=f

4. f'=2f, f''=2f