Question

find the combined power of lens whose focus are 50cm and -40cm

Answer 1

Given :

➛ Two lenses are placed in contact. Focal length of both are 50cm and -40cm respectively.

To Find :

➾ Power of the combination.

Concept :

➢ The equivalent focal length of thin lenses in contact is given by

፨ 1/f = 1/f¹ + 1/f²

where f¹ and f² are focal lengths of individual lenses.

➢ Relation between focal length of lens and power of lens is given by

፨ P = 1/f

Calculation :

✪ Equivalent focal length :

➠ 1/f = 1/f¹ + 1/f²

➠ 1/f = 1/50 - 1/40

➠ 1/f = 10/2000

➠ f = 200cm = 2m

✪ Power of the combination :

⇒ P = 1/f

⇒ P = 1/2

⇒ P = 0.5 D

Answer 2

Given:-

Two lens are placed in contact.

Focal length of the both is 50cm and 40 cm.

To Find:-

Combined power.

Concept:-

The equivalent focal length of thin lenses in contact is given by,

1/f = 1/f^1 + 1/f^2

Relation between focal length of lens and the power of lens is given by,

p = 1/f

Calculations:-

★Equivalent focal length

$\large\implies{\tt{\frac{1}{f}= \frac{1}{f^1}+\frac{1}{f^2}}}$

$\large\implies{\tt{\frac{1}{f}= \frac{1}{50}-\frac{1}{40}}}$

$\large\implies{\tt{\frac{1}{f}= \frac{10}{2000}}}$

$\large\implies{\tt{ f = 200cm = 2m}}$

★ power of the combination

$\large\implies{\tt{p = \frac{1}{f}= \frac{1}{2}}}$

$\large\implies{\tt{0.5D}}$

$\large\underline{\underline{\boxed{\mathtt{\color{plum}{Combined\: poWer = 0.5D}}}}}{\color{orange}{\bigstar}}$