An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

Options

A. 36 cm towards the mirror
B. 30 cm away from the mirror
C. 30 cm towards the mirror
D. 36 cm away from the mirror

Answer

A, C, D

Explanation

`(1)/(v_1)=1/f-(1)/(u_1)=(u_1-f)/(u_1f)`
`therefore v_1=(u_1f)/(u_1-f)=((-40)(-15))/(-40-(-15))`
`therefore v_1=(600)/(-25)=-24` cm
Now `u_2`=-20 cm ,`v_2=?`

`(1)/(v_2)=(1)/(f.)-(1)/(u_2)=(u_2-f)/(u_2f)`
`therefore v_2=(u_2f)/(u_2-f)=((-20)(-15))/(-20-(-15))`
`therefore v_2=(300)/(-5)=-60` cm
Distance between images = `v_2-v_1`
=-60+24
=-36 cm
As distance is positive hence 36 cm away from mirror.