Question

Two thin lenses of power +4D and -2D are in contact. What is the focal length of the combination?

Answer 1

Given :

Two thin lens of power +4D and -2D are placed in contact.

To Find :

We have to find focal length of the combination$.$

SoluTion :

➳ Power of the combination of lens is given by

• P = P¹ + P²

➳ Relation b/w power of lens and focal length is given by

• P = 1/f

✪ Power of the combination :

➝ P = P¹ + P²

➝ P = (+4) + (-2)

➝ P = +2D

✪ Focal length of the combination :

➝ P = 1/f

➝ f = 1/2

➝ f = 0.5m = 50cm

Answer 2

Given ,

• The two thin lenses of power 4 D and -2 D are in contact

We know that ,

The ability of lens to converge or diverge the light rays falling on it is called power of lens

The equivalent power of two lenses in contact is given by

$\boxed{ \sf{P = </p><p>P _{1} + P _{2} }}$

Thus ,

P = 4 + (-2)

P = 4 - 2

P = 2 D

Therefore ,

• The power of combination is 2 D

Now , the reciprocal of power of lens is called focal length

Focal length (f) = 1/P

Thus , the focal length of the combination will be

f = 1/2

f = 0.5 m

Therefore ,

• The focal length of combination is 0.5 m or 50 cm