Question

A student conducts an experiment using a convex lens. he places the object at a distance of 60 cm in front of the lens and observes that the image is formed at a distance of 30 cm behind the lens. the power of the lens is?

Answer 1

$\huge {\underline{\pink{Given:-}}}$

• Object distance , u = -60 cm

• Image distance ,v = 30cm

$\huge {\underline{\green{To Find:-}}}$

• Focal length ,f

$\huge {\underline{\blue{Solution:-}}}$

Firstly we calculate the focal length of the lens.

By using lens formula

• 1/v -1/u = 1/f

where,

v is the image distance

u is the object distance

f is the focal length

Substitute the value we get

➺ 1/30 - 1/(-60) = 1/f

➺ 1/f = 1/30 + 1/60

➺ 1/f = 2+1 /60

➺ 1/f = 3/60

➺ 1/f = 1/20

➺ f = 20cm

Therefore, the focal length of the lens is 20 cm.

Now , we know that Power of lens is defined as the reciprocal of its focal length in metre.

• P = 1/f

Substitute the value we get

➺ P = 1/20/100

➺ P = 100/20

➺ P = 5 D

Therefore, the power of the lens is 5 Dioptre.

Answer 2

Explanation:

Given :

• A student conducts an experiment using a convex lens. he places the object at a distance of 60 cm in front of the lens.

• the image is formed at a distance of 30 cm behind the lens.

To Find :

• the power of the lens is ?

Solution :

Concept :

• A lens formula may be defined as the formula which gives the relationship between the distance of image (v), distance of object (u), and the focal length (f) of the lens. It may be written as: 

Where,  

v   =   Distance of image from optical centre of lens  

u   =   Distance of object from optical centre of lens  

f   =   Focal length of lens 

       The lens formula is applicable both in convex lenses and concave lenses.

➥1/v -1/u = 1/f

Substitute all value :

➦ 1/30 - 1/(-60) = 1/f

➥ 2 + 1 / 60 = 1 / f

➥ 3 / 60 = 1 / f

➥ 3f = 60

➥ f = 60 / 3

➥ f = 20

• the focal length of the lens is 20 cm.

The S.I unit of Power of lens (P) is dioptres (D) and Focal length is to be measured in metres (m) according to the formula you’ve

Given i.e. P = 1/f

If you choose f to be in centimetres (cm), then you must choose the formula, P = 100/f.

[ This is because 1m = 100cm. ]

P = 1/f

Substitute all values :

➦ p = 100 / 20

➦ p = 5 Dioptre

Hence The power of the lens is 5 Dioptre.

more to know :

Power :

• Power is defined as the time rate at which work is done or energy is transferred by it.

Focal length :

• Focal length is the distance between the centre of a lens or curved mirror and its focus.