Question

focal length of a convex lens is 50 cm if the object is kept at 75 cm then find the image distance and magnification​

Answer 1

Question:

Focal length of a convex lens is 50 cm if the object is kept at 75 cm then find the image distance and magnification​.

Answer:

• The image distance is 150 cm.

• The magnification is -2.

Given:

Focal length(f) = 50 cm.

The distance of the object(u) = 75 cm.

To find:

• The distance of the image.
• The magnificent of the image.

Explanation:

Let, the distance of the image be, 'v' from the mirror.

f = 50 cm.

u = 75 cm.

We know that,

$\frac{1}{f} = ( \frac{1}{u} + \frac{1}{v})$

⇒ $\frac{1}{50} = (\frac{1}{75} + \frac{1}{v})$

⇒ $(\frac{1}{50} - \frac{1}{75} ) = \frac{1}{v}$

⇒ $\frac{1}{v} = (\frac{1}{50} - \frac{1}{75})$

⇒ $\frac{1}{v} = (\frac{3 - 2}{150} )$ [∵ The L.C.M. of the denominators is 150.]

⇒ $\frac{1}{v}= \frac{1}{150}$

⇒ v = 150 cm.

∴ The distance of the image is 150 cm.

Let, the magnification be, 'm'.

We know that,

$m = -\frac{v}{u}$

⇒ $m = - \frac{150}{75}$

⇒ $m = -\frac{6}{3}$ [ ∵ Dividing 150 and 75 by 25.]

⇒ $m = -2$ [∵ Dividing 6 and 3 by 3.]

∴ The magnification of the image is -2.

∵Magnification has no unit because it is the ratio of the distance of the image and the distance of the object from the mirror and ratio has no unit.