Question

A convex mirror having radius of curvature 3m is fitted as a rearview mirror in a bus. Find the position,nature and magnification of the image of a car standing behind the bus at 6 m from the mirror.​

Answer 1

Answer:

Complete step by step solution

Given, the bus is located from the convex mirror at the distance, u=−5m

The radius of curvature of the convex mirror, r=+3m

Therefore, the focal length of the convex mirror, f=+32m

According to the mirror formula,

1f=1v+1u

On putting values of each term, we get

1v+(1−5)=23

1v=23+15

1v=10+315=1315

∴ v=1513≈1.1538 m

Since the position of the image is positive. Therefore, the image will form behind the mirror, i.e. the image will be virtual in nature.

Now, according to the magnification formula of the mirror,

m=hIho=−vu

On putting the values of v and u, we get

hI=−⎛⎝⎜⎜1513−1.5⎞⎠⎟⎟ho=1013h