Question

a convex mirror of focal length 3m, with a image distance of 1.3 m and magnification of 0.5 m. find the image distance.​

Answer 1

Given :

In convex mirror,

Focal length : 3m

Object distance : 1.3 m

To find :

The image distance.

Solution :

Now, using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

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

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

By substituting all the given values in the formula,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 1.3} = \dfrac{1}{3}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{1.3} = \dfrac{1}{3}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{3} + \dfrac{1}{1.3}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{13 + 10 }{39}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{23}{39}$

$\dashrightarrow\sf v = \dfrac{39}{23}$

$\dashrightarrow\sf v = 1.69 \: m$

Thus, the position of the image is 1.69 m.

Answer 2

Answer:-

• Focal length=f=3m
• image distance=u=-1.3m
• Magnification=m=0.5m
• Object distance=v=?

We know

■m=h'/h=-v/u

⇨0.5=-v/(-1.3)

⇨0.5=v/1.3

⇨v=1.3×0.5

⇨v=0.65m