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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

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Answer

C. 0.6125 m

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

Answer : v = 0.1625 m.

Explanation :

It is given that,

Height of an object, [tex]h_o=0.4\ m[/tex]

Object distance, [tex]u=-0.7\ m[/tex]

Height of an image, [tex]h_i=0.35\ m[/tex]

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. [tex]m=\dfrac{h_i}{h_o}[/tex]..............(1)

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

i.e [tex]m=\dfrac{-v}{u}[/tex]............(2)

So, from equation (1) and (2)

[tex]\dfrac{-v}{u}=\dfrac{h_i}{h_o}[/tex]

[tex]\dfrac{-v}{-0.7\ m}=\dfrac{0.35\ m}{0.4\ m}[/tex]

[tex]v=0.6125\ m[/tex]

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

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