Question

the image formed by convex mirror is only one third of the size of the object if the focal length of the mirror is 12cm the image formed will be a)8cm behind the mirror b)10cm behind the mirror c)8cm in front of the mirror d) 10cm in front of the mirror ​

Answer 1

Answer:

Given

image formed by a convex mirror is only

one-third of the size of the object.

image formed by a convex mirror is only

one-third of the size of the object. focal

length of the mirror is 12 cm

To find

Image distance (v)

Explanation:

Given,

for a convex mirror,

Focal length=f=12cm

Image formed is 1/3rd the size of the object

hi=ho/3

hi/ho=1/3

but hi/ho is equal to magnification which is also equal to -v/u

therefore

-v/u=1/3

u=-3v..............(1)

Using the formula

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

f

1

=

v

1

+

u

1

$$\begin{lgathered}= > \dfrac{1}{12} = \dfrac{1}{v} + \dfrac{1}{u } \\ \\ = > \dfrac{1}{12} = \dfrac{1}{v} - \dfrac{1}{3v} \\ \\ = > \dfrac{1}{12 } = \dfrac{3 - 1}{3v} \\ \\ = > \dfrac{1}{12} = \dfrac{2}{3v} \\ \\ = > 3v = 24 \\ \\ \boxed{ \sf \: v = 8cm}\end{lgathered}$$

Therefore

the image will be formed 8cm behind the mirror