Question

An object 4cm high is placed at a distance of 15cm in front of a convex mirror having a radius of curvature of 10cm.
Then the image formed is at a distance of
o 7.5cm behind the mirror
0 3.75cm in front of the mirror
o 7.5cm in front of mirror
3.75cm behind the mirror​

Answer 1

Given :

Object height = 4cm

Object distance = - 15cm

Radius of curvature = 10cm

To find :

The image distance.

Solution :

Firstly we have to find the focal length. We know that the radius of curvature is twice the focal length.

R = 2f

10 = 2f

f = 10/2 = 5cm

Now, using mirror formula that is,

The relationship between image distance, object distance and focal length of a spherical mirror is known as Mirror formula.

The mirror formula can be written as :

$\boxed{ \bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

where,

• v denotes image distance.
• u denotes object distance.
• f denotes focal length.

substituting all the given values in the formula,

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} }$

$\leadsto{ \sf \dfrac{1}{v} + \dfrac{1}{( - 15)} = \dfrac{1}{5} }$

$\leadsto{ \sf \dfrac{1}{v} - \dfrac{1}{15} = \dfrac{1}{5} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{1}{5} + \dfrac{1}{15} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{3 + 1}{15} }$

$\leadsto{ \sf \dfrac{1}{v} = \dfrac{4}{15} }$

$\leadsto{ \sf v = \dfrac{15}{4} }$

$\leadsto{ \sf v = 3.75 \: cm}$

In convex mirror image always formed behind the mirror.

thus, option (d) 3.75cm behind the mirror is correct.

Answer 2

Answer:

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