David is observing his image in a plane mirror. The distance between the mirror and his image is 4 m. If he moves 1 m towards the mirror, then the distance between David and his image will be

Ans: $6 \mathrm{m}$

For a plane mirror,

The distance between the object and the mirror (${\mathrm{d}}_1$) is same as the distance between image and mirror (${\mathrm{d}}_2$).

Given,

The distance between the mirror and David’s image, ${\mathrm{d}}_2 = 4 \mathrm{m}$

 $\therefore {\mathrm{d}}_{1 }= {\mathrm{d}}_2 = 4 \mathrm{m}$
 

If David moves $1 \mathrm{m}$ towards the mirror, then ${\mathrm{d}}_1 = 4 - 1 = 3 \mathrm{m}$

Again, 

${\mathrm{d}}_1 = {\mathrm{d}}_2 = 3 \mathrm{m}$

Now, the distance between David and his image is,

$\mathrm{d} = {\mathrm{d}}_1 + {\mathrm{d}}_2$

Substituting the values

$\mathrm{d}= 3 + 3 = 6 \mathrm{m}$

Thus the distance between David and his image, $\mathrm{d} = 6 \mathrm{m}$