Q.a) Two convex lenses of focal lengths f1 and f2 respectively are placed in contact with each other. Then what will be power of their equivalent lens? b) Write down the conditions for constructive interference. c) The refractive index of glass is 1.55. What is its polarising angle? Determine the angle of refraction for the polarising angle.

a) Two thin lenses in contact combine as P = P1+P2. b) Constructive interference occurs where the path difference between the waves is an integral multiple of λ. c) For glass of μ=1.55, the polarising (Brewster) angle is ≈57.2° and the corresponding angle of refraction is ≈32.8°.

a) Power of two convex lenses in contact: For thin lenses in contact, the powers simply add:

$P = P_1+P_2 = \dfrac{1}{f_1}+\dfrac{1}{f_2}$

Equivalently, the equivalent focal length is $f=\dfrac{f_1f_2}{f_1+f_2}$.

b) Conditions for constructive interference: Two coherent waves interfere constructively at a point where they arrive in phase, i.e. where the path difference between them is an integral (whole) multiple of the wavelength:

$\Delta = n\lambda, \quad n=0,1,2,\dots$

equivalently a phase difference of $2n\pi$. (For good contrast the two waves should also have comparable/equal amplitude.)

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