Question

A concave mirror (focal length 15 cm) and a convex mirror (focal length 10 cm) are placed co-axially 70 cm apart facing each other. A 2 cm tall object is placed perpendicular to the common axis 20 cm from the concave mirror. How far from the convex mirror is the final image formed by two reflections, first at concave mirror and then at convex mirror?

Solution

Correct option is

5 cm

 

The concave mirror forms a real image A’B’ of the object AB. The imageA’B’ acts as a virtual object for the convex mirror forming the final image at A”B”.

For reflection at concave mirror 

                            

                          

or                       v1 = – 60 cm

for reflection at convex mirror    

                                              

                        

or                    v2 = +5 cm.  

SIMILAR QUESTIONS

Q1

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?   

Q2

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?   

Q3

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

Q4

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? 

Q5

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?

Q6

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?

Q7

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? 

Q8

 

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? 

Q9

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  

Q10

A motor car is fitted with a convex driving mirror of focal length 20 cm. A second motor car 2.1 m broad and 1.05 m high is 4 m behind the first car. What is the size of the image of the second car as seen in the mirror of the first?