Question

If the focal length of the lens is 8 cm and object is placed at 12 cm from optical centre the image will be formed at
(a) 2.4 cm from O
(b) 4.8 cm from O
(c) 24 cm from O
(d) 48 cm from O​

Answer 1

Answer:

- 24

Explanation:

Focal length of convex lens,  f = 8 cm

Object distance,  u = 12 cm

Using lens formula    1/v − 1/u = 1/f

where v is the image distance.

∴  1/v - 1/12 = 1/8

⟹ v= -24 cm

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Answer 2

The correct answer to the question is Option (c),

i.e., the image will be formed at a distance of 24 cm from O.

Given:

The focal length of the lens (f) is = 8 cm.

The distance of the object from the optical center (u) = 12 cm.

To Find:

The distance of the image formed from the optical center is (v) =?

Solution:

A lens is a transparent medium bounded either by two surfaces or by a single surface.

Assuming the lens given above to be a convex lens as the focal length given is 8cm. i.e., f = +8cm

And as per the sign convention, the object distance is always assumed to be with a negative i.e., u = -12 cm.

We have the lens formula to calculate the image distance as follows;

$\frac{1}{v}$ - $\frac{1}{u}$ = $\frac{1}{f}$

∴ $\frac{1}{v}$ =  $\frac{1}{f}$ +  $\frac{1}{u}$

∴ $\frac{1}{v}$ =  $\frac{1}{8}$ + $\frac{1}{(-12)}$

∴ $\frac{1}{v}$ =  $\frac{1}{8}$ - $\frac{1}{12}$

∴ $\frac{1}{v}$ =  $\frac{12-8}{(12)(8)}$

∴ $\frac{1}{v}$ =  $\frac{4}{96}$

∴ $\frac{1}{v}$ =  $\frac{1}{24}$

∴ v = 24 cm.

Thus, the image formed will be at a distance of 24 cm from the optical center O.

Learn more about lens formula at:

https://brainly.in/question/7778719

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