A concave mirror of focal length \(100\) cm is used to obtain the image of the sun which subtends an angle of $\mathrm{}$\(30'.\) The diameter of the image of the sun will be:
1. \(1.74\) cm
2. \(0.87\) cm$$
3. \(0.435\) cm$$
4. \(100\) cm

A square of side 3 cm  is placed at a distance of 25 cm from a concave mirror of focal length 10 cm. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is:

A ray of light falls on the surface of a spherical glass paperweight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$ . The angle of deviation of the emergent ray from the direction of the incident ray

(a) $\left(\alpha -\beta \right)$                     (b) $2\left(\alpha -\beta \right)$

(c) $\left(\alpha -\beta \right)/2$                 (d) $\left(\beta -\alpha \right)$

Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face what so ever be the value of angle of incidence 

(1) $n>\sqrt{2}$                       

(2) $n=1$

(3) $n=1.1$                       

(4) $n=1.3$

One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 10 cm behind the silvered face. The refractive index of the glass is [Consider that light ray returns back in the first medium]

(1) 0.4                     

(2) 0.8

(3) 1.5                     

(4) 1.6

Two transparent slabs have the same thickness as shown. One is made of material A of refractive index 1.5. The other is made of two materials B and C with thickness in the ratio 1:2. The refractive index of C is 1.6. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both, the refractive index of B is

1.  1.1     

2.  1.2

3.  1.3

4.  1.4

The image of point P when viewed from the top of the slabs will be

(1)   2.0 cm above P

(2)   1.5 cm above P

(3)   2.0 cm below P

(4)   1 cm above P

Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place?

$$\begin{gathered} \mathrm{There} \mathrm{is} \mathrm{an} \mathrm{equi}-\mathrm{convex} \mathrm{glass} \mathrm{lens} \mathrm{with} \mathrm{radius} \mathrm{of} \mathrm{each} \mathrm{face} \mathrm{as} \mathrm{R} \mathrm{and} {\mathrm{\mu }}_{\mathrm{ga}}=\frac{3}{2} \mathrm{and} \\ {\mathrm{\mu }}_{\mathrm{wa}}=\frac{4}{3}. \mathrm{If} \mathrm{there} \mathrm{is} \mathrm{water} \mathrm{in} \mathrm{object} \mathrm{space} \mathrm{and} \mathrm{air} \mathrm{in} \mathrm{image} \mathrm{space}, \mathrm{then} \mathrm{the} \mathrm{focal} \mathrm{length} \\ \mathrm{is} : \end{gathered}$$

(1)   2R                                     

(2)   R

(3)   $\frac{3}{2}R$                                 

(4)  $R^2$

A prism having an apex angle 4^o and refraction index 1.5 is located in front of a vertical plane mirror as shown in the figure. Through what total angle is the ray deviated after reflection from the mirror?

(a)   176^o

(b)   4^o

(c)   178^o

(d)   2^o