Question

An object placed in front of a plane mirror is displaced by$0.4$ $m$ along a straight line at an angle of ${30}^{\circ }$ to mirror plane. The change in the distance between the object and its image is

• A. $0.20m$
• B. $0.40m$
• C. $0.25m$
• D. $0.70m$

Answer 1

The correct option is B $0.40m$

From the diagram,

The distance between the image and object is given as

$d_1=u+u=2u$

Now when the object is displaced by $0.04cm$ parallel to the line which is making ${30}^{\circ }$ an angle with mirror, hence the new distance becomes

$d_2=0.4\cos {60}^{\circ }+0.4\cos {60}^{\circ }+2u$

$d_2=0.4\times \frac{1}{2}+0.4\times \frac{1}{2}+2u$

$d_2=0.2+0.2+2u$

$d_2=0.4+2u$

Now the change in the distance between the object and image is given as

$d_2-d_1=0.4+2u-2u$

$d_2-d_1=0.4m$.