Question

A double convex lens with refractive index μ₁ inside two liquids of refractive indices μ₂ and μ₃ are shown in the diagrams below. The refractive indices are such that μ₂ > μ₁ and μ₁ > μ₃.

Figure a	Figure b

How would a parallel incident beam of light refract when it comes out of the lens in each of the cases shown above?

1. in Fig a.
2. in Figure b.

Answer 1

According to the lens maker formula:

`1/f ∝ ("refractive index of 2nd medium"/"refractive index of 1st medium" - 1)`   .....(i)

1. In figure a:

Refractive index of 1st medium = μ₃

Refractive index of 2nd medium = μ₁

Then, from relation (i)

`1/f ∝ (μ_1/μ_3 - 1)`

As, μ₁ > μ₃

⇒ `μ_1/μ_3 > 1`

⇒ `1/f > 0`

⇒ f > 0

Since the resulting focal length is positive so this lens behaves as a converging lens.

Hence, a parallel incident beam of light converges when it comes out of the lens im figure a.

2. In figure b:

Refractive index of 1st medium = μ₂

Refractive index of 2nd medium = μ₁

Then, from relation (i)

`1/f ∝ (μ_1/μ_2 - 1)`

As, μ₁ < μ₂

⇒ `μ_1/μ_2 < 1`

⇒ `1/f < 0`

⇒ f < 0

Since the resulting focal length is negative, this lens behaves as a diverging lens.

Hence, a parallel incident beam of light diverges when it comes out of the lens in figure b.