Answer to Question #187656 in Optics for Anas

Question

Convex lens is illuminated by a plane wave which is propagating along z-axis. Sketch and nd out

mathematical expressions of wavefronts within each part of the optical system. Focus of both lenses are

f. The pattern t(x; y) is given as 1/2*[1+ cos(2x=10)]

Answer 1

Given data:

Pattern $t(x,y)=\dfrac{1}{2}[1+cos(2\pi x/10)]$

$= \frac{1}{2}[2cos^2(\frac{\pi x}{10})]=cos^2(\pi x/10)$

(a) Wave front behavior at f

$\bar u =-f$ [wave focus on focal point means intense wave form arises at focal point]

$\dfrac{1}{v}-\dfrac{1}{(-f)}=\dfrac{1}{f}\\\Rightarrow \dfrac{1}{v}=0\\\Rightarrow v= \infty$

Image at infinity but density is squared

(b) Wave front behavior at 2f

[On 2f position wave normalize the wave front ]

$\bar u =-2f\\\dfrac{1}{v}=\dfrac{1}{u}+\dfrac{1}{f}=\dfrac{1}{(-3f)}+\dfrac{1}{f}=\dfrac{2}{3f}\\\Rightarrow So\ Size = (\dfrac{3}{2})times$

As the wave front is squared , So it is always it the positive direction

$\dfrac{-v}{u}=\dfrac{3}{2}$ [At 2f] ; $\dfrac{-v}{u}=\infty$ [At f]

(Magnification here infinity represent the order of t(x,y) is vary much less than order at f)