A concave lens forms the image of an object such that the distance between the object and image is 10 cm. If magnification of the image is $\frac{1}{4}$. The focal length of the lens is

(1) 6 cm

(2) $\frac{20}{3}<mspace\; width="1em"></mspace>cm$

(3) $\frac{10}{7}<mspace\; width="1em"></mspace>cm$

(4) $\frac{40}{9}$

When an object is placed at 10 cm and 30 cm from a convex lens images obtained are of the same magnitude of magnification. The focal length of the lens maybe:

(1) 10 cm

(2) 15 cm

(3) 20 cm

(4) 25 cm

To increase the magnifying power of a telescope:

A ray of light is incident on a prism of angle A and refractive index $\mu$ will not emerge out of prism for any angle of incidence, if

(1) $\mu >\sin \frac{A}{2}$

(2) $\mu >\cos <mspace\; width="1em"></mspace>A$

(3) $\mu <\frac{1}{\sin <mspace\; width="1em"></mspace>A}$

(4) $\mu >\frac{1}{\sin <mspace\; width="1em"></mspace>{\displaystyle \frac{A}{2}}}$

What should be the maximum angle of acceptance at the air core interface of an optical fiber, if $n_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>n_2$ are the refractive indices of the core and the cladding respectively?

(1) ${\sin }^{-1}\left(\frac{n_2}{n_1}\right)$

(2) ${\sin }^{-1}\sqrt{n_1^2-n_2^2}$

(3) ${\tan }^{-1}\left(\frac{n_2}{n_1}\right)$

(4) ${\sin }^{-1}\left(\frac{n_1}{n_2}\right)$

Two positions of the convex lens for which the image of the object is formed on the same screen are 40 cm and 80 cm from the object. The focal length of the lens is

1.  $\frac{80}{3}cm$

2.  $\frac{40}{3}cm$

3.  40 cm

4.  80 cm

A person cannot see objects clearly that are closer than 2 m and farther than 4 m. To correct the eye vision, the person will use:

(1) Bifocal lenses of power -3.5 D and 0.25 D

(2) Bifocal lenses of power -0.25D and 3.5 D

(3) Bifocal lenses of power -0.5D and 4.0D

(4) Bifocal lenses of power -4.0D and 0.5 D

A graph is plotted between the angle of deviation $\delta$ in a triangular prism and the angle of incidence as shown in the figure. Refracting angle of the prism is: 

 
1. \(28^\circ\)
2. \(48^\circ\)
3. \(36^\circ\)
4. \(46^\circ\)