The focal lengths for violet, green, and red light rays are ${\mathrm{f}}_{\mathrm{V}}, {\mathrm{f}}_{\mathrm{G}}, \mathrm{and} {\mathrm{f}}_{\mathrm{R}}$ respectively. Which of the following is the true relationship?

1.  ${\mathrm{f}}_{\mathrm{R}}$ < ${\mathrm{f}}_{\mathrm{G}}$ < ${\mathrm{f}}_{\mathrm{V}}$

2.  ${\mathrm{f}}_{\mathrm{V}}$ < ${\mathrm{f}}_{\mathrm{G}}$ < ${\mathrm{f}}_{\mathrm{R}}$

3.  ${\mathrm{f}}_{\mathrm{G}}$ < ${\mathrm{f}}_{\mathrm{R}}$ < ${\mathrm{f}}_{\mathrm{V}}$

4.  ${\mathrm{f}}_{\mathrm{G}}$ < ${\mathrm{f}}_{\mathrm{V}}$ < ${\mathrm{f}}_{\mathrm{R}}$

A plane mirror is placed at the bottom of a tank containing a liquid of refractive index $\mathrm{\mu }$. P is a small object at a height h above the mirror. An observer O vertically above P outside the liquid sees P and its image in the mirror. The apparent distance between these two will be:

1.  $2\mathrm{\mu h}$

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

3.  $\frac{2\mathrm{h}}{\mathrm{\mu } - 1}$

4.  $\mathrm{h}\left(1 + \frac{1}{\mathrm{\mu }}\right)$

When the rectangular metal tank is filled to the top with an unknown liquid, an observer with eye level with the top of the tank can just see the corner E; a ray that refracts towards the observer at the top surface of the liquid is shown. The refractive index of the liquid will be:

1.  1.2

2.  1.4

3.  1.6

4.  1.9

A concave mirror and a converging lens (glass with $\mathrm{\mu } = 1.5$) both have a focal length of 3 cm when in air. When they are in the water $\left(\mathrm{\mu } = \frac{4}{3}\right)$, their new focal length are:

1.  ${\mathrm{f}}_{\mathrm{Lens}} = 12 \mathrm{cm}, {\mathrm{f}}_{\mathrm{Mirror}} = 12 \mathrm{cm}$

2.  ${\mathrm{f}}_{\mathrm{Lens}} = 3 \mathrm{cm}, {\mathrm{f}}_{\mathrm{Mirror}} = 12 \mathrm{cm}$

3.  ${\mathrm{f}}_{\mathrm{Lens}} = 3 \mathrm{cm}, {\mathrm{f}}_{\mathrm{Mirror}} = 3 \mathrm{cm}$

4.  ${\mathrm{f}}_{\mathrm{Lens}} = 12 \mathrm{cm}, {\mathrm{f}}_{\mathrm{Mirror}} = 3 \mathrm{cm}$

A soldier directs a laser beam on an enemy by reflecting the beam from a mirror. If the mirror is rotated by an angle $\mathrm{\theta }$, by what angle will be reflected beam rotate?

1.  $\mathrm{\theta }$/2

2.  $\mathrm{\theta }$

3.  2$\mathrm{\theta }$

4.  None of these

When an object is at a distance of ${\mathrm{\mu }}_1 \mathrm{and} {\mathrm{\mu }}_2$ from the poles of a concave mirror, images of the same size are formed. The focal length of the mirror is:

1.  ${\mu }_1 + {\mu }_2$

2.  ${\mu }_1 - {\mu }_2$

3.  $\frac{{\mu }_1 + {\mu }_2}{2}$
4.  $\frac{{\mu }_1 - {\mu }_2}{2}$

A given ray of light suffers minimum deviation in an equilateral prism P. Additional prism Q and R of identical shape and of the same material as P is now added as shown in the figure. The ray will now suffer:

1.  greater deviations 

2.  no deviation

3.  same deviation as before 

4.  total internal reflection

For a spherical mirror, the graph of 1/v versus 1/u is given by:

1.  

2.  

3.  

4.  

The focal length of the objective and the eyepiece of a microscope are 4 mm and 25 mm respectively. If the final image is formed at infinity and the length of the tube is 16 cm, then the magnifying power of the microscope will be:

1.  -327.5

2.  -3.75

3.  3.3275

4.  32.75

The figure shows a concavo-convex lens. What is the condition on the refractive indices so that the lens is diverging?

1. $2{\mu }_3<{\mu }_1+{\mu }_2$

2. $2{\mu }_3>{\mu }_1+{\mu }_2$

3. ${\mu }_3>2({\mu }_1-{\mu }_2)$

4. None of these