Question

the convergent lens of power 5 D is combined with divergent lens of power -4 D. then, find the focal length and power of combination of both the lenses.​

Answer 1

The focal length and power of combination of both the lenses is 100 cm and 1 D respectively.

Explanation:

Power of the convergent lens,  $P_1=5\ D$

Power of the divergent lens, $P_2=-4\ D$

The power of the combination is given by the sum of powers of individual lens. It is given by :

$P=P_1+P_2$

$P=5-4=1\ D$

The relation between the power and the focal length is given by :

$f=\dfrac{1}{P}$

f = 1 m

or

f = 100 cm

Hence, the focal length and power of combination of both the lenses is 100 cm and 1 D respectively.

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Answer 2

Answer:

Explanation:

Given :-

P₁ = 5D

f₁ = 100/5 = 20 cm

P₂ = - 4D

f₂ = 100/- 4 = - 25 cm

Solution :-

if F be the combination of both lenses, then

1/F = 1/f₁ + 1/f₂

⇒ 1/F = 1/20 - 1/25

⇒ 1/F = 5 - 4/100

⇒ 1/F = 1/100

⇒ F = 100 cm

Hence, the focal length is 100 cm.

Power of combination of both lenses,

P = 1/F(in metre)

⇒ P = 100/F(cm

⇒ P = 100/100

⇒ P = 1 D

Hence, the power of combination of both the lenses is 1D.