A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1=n2=n. The focal length is f+Δf when n1=n and n2=n+Δn. Assuming Δn<<(n−1) and (1<n<2), the correct statement(s) is/are?<p></p>

A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1=n2=n. The focal length is f+Δf when n1=n and n2=n+Δn. Assuming Δn<<(n−1) and (1<n<2), the correct statement(s) is/are?

If Δn<0, then Δf/f>0

The relation between Δf/f and Δn remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature

|Δf/f|<|Δn|

For n=1.5, Δn=10⁻³ and f=20cm, the value of |Δf| will be 0.02cm (round off to 2nd decimal place)

Solution:

Correct option is D. The relation between Δf/f and Δn remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature
1/f₀ = 2(n−1)/R (1)
1/f₁ = (n−1)(1/R − 1/∞)
1/f₂ = (n+Δn−1)(1/R − 1/∞)
1/f₀ + Δf₀ = (n−1)/R + (n+Δn−1)(1/R)
1/f₀ + Δf₀ = (2n + Δn − 2)/R (2)
(1)/(2) ⇒ (f₀ + Δf₀)/f₀ = (2(n−1)/R)/(2n + Δn − 2)/R
1 + Δf₀/f₀ = 2(n−1)/(2n + Δn − 2)
Δf₀/f₀ = −Δn/(2n + Δn − 2)
Δf₀/20 = −10⁻³/3 + 10⁻³ − 2
⇒ Δf₀ = −2 × 10⁻³
|Δf₀| = 0.02cm.

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