Question

An object is placed at 40cm on a principle axis of a concave mirror and image is
formed at 40 cm from the pole. Draw the ray diagram and write the characteris-
tics of image and calculate the focal length of the mirror. P​

Answer 1

Answer:

2.5cm

Explanation:

Given: An object is placed at a distance of 40 cm on the principal axis of a concave mirror of radius of curvature 30 cm .  

To find the distance by which the image move if the object is shifted towards the mirror through 15 cm

Solution:

As per the given criteria,

Radius of curvature, R=−30cm

So, the focal length, f=  

2

R  

=  

2

−30  

=−15cm

object distance, u=−40cm

Applying the lens formula, we get

f

1

​

=  

v

1

​

+  

u

1

​

⟹  

(−15)

1  

=  

v

1

​

+  

(−40)

1

​  

⟹  

v

1

​

=  

(−15)

1

​

+  

(40)

1

​

 

⟹  

v

1

​

=  

120

−8+3

​

 

⟹v=−24cm

The distance between the image and the mirror is 24cm when the object distance is 40cm.

Now, the object is moved 15cm towards the mirror, so the new object distance is u  

′

=−(40−15)=−25cm

Now applying the lens formula we get,

f

1

​

=  

v  

′

 

1

​

+  

u  

′

 

1

​

 

⟹  

(−15)

1

​

=  

v  

′

 

1

​

+  

(−25)

1

​

 

⟹  

v  

′

 

1

​

=  

(−15)

1

​

+  

(25)

1

​

 

⟹  

v  

′

 

1

​

=  

75

−5+3

​

 

⟹v=−37.5cm

is the new position of the image

So the shift in the position of the image is =40−37.5=2.5cm