Question

A concave mirror has a focal length of 20 cm. Find the position or positions of an object for
which the image size is double of the object-size.

Answer 1

Answer:

The focal length of the mirror is 20cm.

In the case of real image,

The object distance is u  

1

​  

, then the image distance will be −2u  

1

​  

.

The mirror formula is given as,

v

1

​  

+  

u

1

​  

=  

f

1

​  

 

−2u  

1

​  

 

1

​  

−  

u  

1

​  

 

1

​  

=  

20

−1

​  

 

u  

1

​  

=30cm

In the case of virtual image,

The object distance is −u  

2

​  

, then the image distance will be 2u  

2

​  

.

The mirror formula is given as,

v

1

​  

+  

u

1

​  

=  

f

1

​  

 

2u  

1

​  

 

1

​  

+  

−u  

1

​  

 

1

​  

=  

20

−1

​  

 

u  

2

​  

=10cm

The distance between two positions of object is given as,

u=30−10

=20cm

Thus the distance between the two positions of object is 20cm.