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Homework Statement
Part (a):Sketch zeroth and first order rays. Find the angle of first order rays make to normal.
Part (b): Sketch intensity distribution at 7.5mm and 10mm.
Part (c): Explain how this is useful in understanding a microscope.
Homework Equations
The Attempt at a Solution
Part (a)
Using ##d sin\theta = n\lambda##, ##\theta = 2.9^o##. Thus angle to normal is 87.1o.
Part (b)
At 7.5mm
Intensity distribution is given by:
[tex]I = I_0 \frac{sin \left(\frac{Nkd sin\theta}{2}\right)}{sin \left(\frac{kd sin\theta}{2}\right)}[/tex]
Principal Maximas occur at ##\theta_{max} = \frac{n\lambda}{d}##. Separation between a principal maxima and a minima is ##\frac{\lambda}{16d}##.
At 10mm
There will be bright spots separated by distances ##a##. This is equivalent to a N-slit grating. To find a:
[tex]a = \theta f = f \frac{\lambda}{d}[/tex]
[tex]d' = f\frac{\lambda}{a} = d[/tex]
Thus we see that at 10mm, the image of the grating slit is simply reproduced. If we observe at distances greater than 10mm, ##d' > d## is amplified.
Part (c)
By varying the distances of the final plane, we can set the magnification and is given by ##\frac{v}{u}## where ##v## is distance from lens to final plane, ##u## is distance from lens to grating.
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