Question

A convex mirror of focal length 20 cm forms image of magnification 3/5 for one position of the object. The object is shifted by 16/3 cm towards the mirror. By what distance and what direction the image will move

Answer 1

Focal length of mirror is-40 cm (‘-’ sign because it is a concave mirror)

Magnification= m = −vu=4−vu=4

−v=4u−v=4u

v=−4uv=−4u

now , by lens makers formula

1u+1v=1f1u+1v=1f

uvu+v=fuvu+v=f

puttingv=−4u,v=−4u,

It becomes,

−4u2−3u=−40−4u2−3u=−40

−4u−3=−40−4u−3=−40

u=−30u=−30

putting u=−30u=−30in v=−4uv=−4u

we get v=120cm


hope it helps