Question

An object that has a height of 0.4 meter is placed at a distance of 0.7 meter from a concave spherical mirror. An image is formed in front of the mirror and has a height of 0.35 meter. How far from the mirror is the image located?

A. 0.2000 m
B. 0.4275 m
C. 0.6125 m
D. 0.8000 m

Answer 1

Answer : v = 0.1625 m.

Explanation :

It is given that,

Height of an object,
`h_o=0.4\ m`

Object distance,
`u=-0.7\ m`

Height of an image,
`h_i=0.35\ m`

We have to find the image distance (v).

We know that the magnification of mirror is the ratio of height of image to the height of object.

i.e.
`m=(h_i)/(h_o)`..............(1)

Also, magnification is the ratio of image distance to that of object distance.

i.e
`m=(-v)/(u)`............(2)

So, from equation (1) and (2)

`(-v)/(u)=(h_i)/(h_o)`

`(-v)/(-0.7\ m)=(0.35\ m)/(0.4\ m)`

`v=0.6125\ m`

So, image is located at a distance of 0.6125 m.

Answer 2

C. 0.6125 m

Step-by-step explanation

The magnification of an image produced by curved mirrors can be given in two ways;

Magnification, M = (Height of the image) / (height if the object) and

M = (image distance,V) / (Object distance, U).

Using the first formula,

M = 0.35/0.4

= 0.875

Now from the second formula,

M = V/U

0.875 = V/0.7

V = 0.875 × 0.7

= 0.6125 m