A thin convex lens is made of two materials with refractive indices $$n_1$$ and $$n_2$$, 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 $$n_1=n_2=n$$. The focal length is $$f+\Delta f$$ when $$n_1=n$$ and $$n_2=n+\Delta n$$. Assuming $$\Delta n << (n-1)$$ and $$(1 < n < 2)$$, the correct statement(s) is/are?
Correct option is D. The relation between $$\dfrac{\Delta f}{f}$$ and $$\dfrac{\Delta n}{n}$$ remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature
$$\dfrac{1}{f_0}=\dfrac{2(n-1)}{R}$$ $$(1)$$
$$\dfrac{1}{f_1}=(n-1)\left(\dfrac{1}{R}-\dfrac{1}{\infty}\right)$$
$$\dfrac{1}{f_2}=(n+\Delta n-1)\left(\dfrac{1}{R}-\dfrac{1}{\infty}\right)$$
$$\dfrac{1}{f_0+\Delta f_0}=\dfrac{(n-1)}{R}+(n+\Delta n-1)\left(\dfrac{1}{R}\right)$$
$$\dfrac{1}{f_0+\Delta f_0}=\dfrac{2n+\Delta n-2}{R}$$ .$$(2)$$
$$(1)/(2)$$
$$\Rightarrow \dfrac{f_0+\Delta f_0}{f_0}=\dfrac{\dfrac{2(n-1)}{R}}{\dfrac{2n+\Delta n-2}{R}}$$
$$1+\dfrac{\Delta f_0}{f_0}=\dfrac{2(n-1)}{2n+\Delta n-2}$$
$$\dfrac{\Delta f_0}{f_0}=\dfrac{-\Delta n}{(2n+\Delta n-2)}$$
$$\dfrac{\Delta f_0}{20}=-\dfrac{10^{-3}}{3+10^{-3}-2}$$
$$\Rightarrow \Delta f_0=-2\times 10^{-2}$$
$$|\Delta f_0|=0.02$$cm.
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:
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:
For a prism of prism angle θ=60∘, the refractive indices of the left half and the right half are, respectively, n1 and n2(n2≥n1) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n1=n2=n=1.5. For the case of unequal refractive indices, n1=n and n2=n+Δn (where, Δn<<n), the angle of emergence e=i+Δe. Which of the following statement(s) is (are) correct ?
