Question

A long horizontal mirror is next to a vertical screen(see figure). Parallel light rays are falling on the mirror at an angle $\alpha$ from the vertical. If a vertical object of height h is kept on the mirror at a distance d $>$ h $tan\left(\alpha \right)$. The length of the shadow of the object on the screen would be.

• A. $h/2$
• B. $h\tan \left(\alpha \right)$
• C. $2h$
• D. $4h$

Answer 1

The correct option is C $2h$

It can be concluded from the attached ray diagram that on the screen, portion $AB$ will be shadow on the screen.

From laws of reflection,

$\angle OCA=\theta$

$\angle OCA={90}^o-\alpha$

$OA=OC\tan \theta$

$OA=(OD-CD)\cot \alpha$

$OA=(d-h\tan \alpha )\cot \alpha$

$OA=d\cot \alpha -h........\left(i\right)$

$OB=OE\tan \theta$

$OB=(OD+ED)\tan \theta$

$OB=(d+h\cot \theta )\tan \theta$

$OB=d\cot \alpha +h..........\left(ii\right)$

Length of shadow,

$AB=OB-OA=2h$