Question

 

The sun’s disc subtends an angle of 10–2 rad at the earth. What must be radius of curvature of the mirror which will produce on a screen an image of the sun 2 cm in diameter? 

Solution

Correct option is

4 m

 

Since the image is formed on a screen, it must be real. Hence the mirror used is concave. Since the distance of the sun is very large (effectively infinite), the image of the sun is formed at the focal plane of the mirror, i.e., the image is at a distance equal to the focal length (f) from the mirror.

                          AB = diameter of the disc of the sun   

                       A’B’ = diameter of the image = 2 cm  

Angle subtended by the disc of the sun = θ = 10 –2 rad

In triangle APO we have

                      

Since OP >> AP, angle θ is very small. Hence  where θ is expressed in radians. Thus

                           

or                      

Now triangles APO and A’P’O are similar. Therefore,   

                 

  

 

SIMILAR QUESTIONS

Q1

A pin is placed 10 cm in front of a convex lens of focal length 20 cm and refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature of 22 cm. How far from the lens is the final image formed?       

Q2

The radius of curvature of the convex face of a plano-convex lens is 12 cm and its refractive index is 1.5. What is the focal length of the lens?

Q3

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?   

Q4

Two glasses have dispersive powers in the ratio of 2 : 3. These glasses are used in the manufacture of an achromatic objective of focal length 20 cm. What are the focal lengths of the two lenses of the objective?   

Q5

An object 5 cm tall is placed 10 cm from a convex mirror. What is the nature and the size of the image?

Q6

A convex mirror of radius of curvature 20 cm forms an image which is half the size of the object. How far is the object from the mirror? 

Q7

How far should an object be held from a concave mirror of focal length 40 cm so as to obtain an image twice the size of the object?

Q8

A concave mirror produces a real image twice the size of the object when place at a distance of 22.5 cm from it. At what distance from the mirror should the object be placed so that the image becomes three times the size of the object?

Q9

Two objects A and B when placed in turn in front of a concave mirror of focal length 7.5 cm, give images of equal size. If A is three times the size ofB and is placed 30 cm from the mirror, what is the distance of B from the mirror? 

Q10

A small strip of plane mirror A is set with its plane normal to the principal axis of a convex mirror B and placed 15 cm in front of B which it partly covers. An object is placed 30 cm from A and the two virtual images formed by reflection in A and B concide without parallax. Find the radius of curvature of B