Question

4.
a) Discuss Rayleigh’s criterion for resolving power of an optical instrument. Obtain an
expression for the resolving power of a microscope.

b) A He-Ne laser emits a beam of diameter 2×10−3m and wavelength 630 nm. It is directed
towards an aeroplane flying at a height of 11 km. Calculate the diameter of the light patch
produced on the surface of the aeroplane.

Answer 1

Answer on Question #50696, Physics, Optics

a) Discuss Rayleigh's criterion for resolving power of an optical instrument. Obtain an expression for the resolving power of a microscope.

b) A He-Ne laser emits a beam of diameter $2 \times 10^{-3} \mathrm{~m}$ and wavelength $630 \mathrm{~nm}$ . It is directed towards an aeroplane flying at a height of $11 \mathrm{~km}$ . Calculate the diameter of the light patch produced on the surface of the aeroplane.

Answer:

a) The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.

b)

Fig.1

See Fig.1

$$d = D + 2 \frac {\lambda}{D} L = 2 \cdot 1 0 ^ {- 3} + 2 \cdot \frac {6 3 0 \cdot 1 0 ^ {- 9}}{2 \cdot 1 0 ^ {- 3}} \cdot 1 1 \cdot 1 0 ^ {3} = 6. 9 3 m$$

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