Question

Two thin lenses of power +3.5 D and -2.5 D are placed in contact. Find the
focal length of the lens combination.
a) 10cm
b) -1cm
c) 100cm
d) 0.001cm

Answer 1

Answer :-

Focal length of the lens combination is 100 cm [Option.c] .

Explanation :-

We have :-

→ Power of 1st lens (P₁) = + 3.5 D

→ Power of 2nd lens (P₂) = -2.5 D

To find :-

→ Focal length of the combination .

______________________________

Focal length of 1st lens :-

⇒ P₁ = 1/f₁

⇒ f₁ = 1/P₁

⇒ f₁ = 1/3.5

⇒ f₁ = 10/35 metre

Focal length of 2nd lens :-

⇒ f₂ = 1/P₂

⇒ f₂ = 1/(-2.5)

⇒ f₂ = 10/(-25)

⇒ f₂ = -10/25 metre

______________________________

Now, focal length (equivalent) of the combination will be :-

1/f = 1/f₁ + 1/f₂

⇒ 1/f = 1/(10/35) + 1/(-10/25)

⇒ 1/f = 35/10 - 25/10

⇒ 1/f = 10/10

⇒ f = 1 m

⇒ f = 100 cm

Answer 2

Answer:

Explanation:

Answer :-

Focal length of the lens combination is 1 m

Solution -

Focal length of 1st lens :-

➥ P₁ = 1/f₁

➥ f₁ = 1/P₁

➥ f₁ = 1/3.5

➥ f₁ = 10/35 metre

Focal length of 2nd lens :-

➥f₂ = 1/P₂

➥ f₂ = 1/(-2.5)

➥ f₂ = 10/(-25)

➥ f₂ = -10/25 metre

Now to find focal length-

1/f = 1/f₁ + 1/f₂

➥1/f = 1/(10/35) + 1/(-10/25)

➥1/f = 35/10 - 25/10

➥ 1/f = 10/10

➥f = 1 m

➥ f = 100 cm