(i)
Two thin lenses, of focal length f1 and f2 are kept in contact. Let O be the position of object Let u be the object distance. The distance of the image (which is at I1) for the first lens is v1.
This image serves as object for the second lens. let the final image be at I.
We than have.
\(\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}\)
\(\frac{1}{f_2}=\frac{1}{v}-\frac{1}{v_1}\)
Adding, we get
\(\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
\(∴\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\)
∴ P = P1 + P2
(ii) At minimum deviation
\(r=\frac{A}{2}\) = 30°
We are given that
\(i=\frac{3}{4}A=45°\)
\(∴μ=\frac{sin\,45°}{sin\,30°}=√2\)
∴ Speed of light in the prism = \(\frac{c}{√2}\)
(≅ 2.1 × 108 ms-1)
[Award ½ marks if the student writes the formula: \(μ=\frac{sin(A+δ_m)/2}{sin(A/2)}\) but does not do any calculations.]