A simple reflective microscope as shown at left below can be made from a concave

Question

A simple reflective microscope as shown at left below can be made from a concave spherical reflector of radius R = 10cm and aperture diameter D = 1cm, held in a glass cup, and viewed from above with the naked eye. If a small sample is held at the height equal to the focal length of the mirror, the object will be appear to be infinitely distant (similar to using a refractive lens as a magnifying glass). Assuming the light is wavelength 550nm (green): What is the height H for an empty cup, so the object will appear to be at infinity? What is the diffraction limited spatial resolution of this lens? If the cup were filled with water (n=l 33), how would your answer to 1 & 2 change?

Explanation / Answer

1) The equation of a typical concave sperical mirror can be written as;

1/f = 1/O + 1/I

where f is the focal length, O is object distance and I is the image distance.

image of the object should be in infinity; so I = infinity; which depicts

f = O = 10 cm.

So if the object is placed at the distance equal to the radius of the mirror, then the image is formed at infinity.

2) The diffraction limited spatial resolution (R) can be represented as;

R = wavelength/(2*n*sin(theta))

where n = 1 as the medium is air

theta = 1.22 * wavelength / Diameter = 6.71*10-5 rad.

Then R = 0.2

3)if the cup is filled with water (n = 1.33),

The Height H of the empty cut will not change bacause it is not depend on n.

But the diffraction limited spatial resolution (R) will be changed slightly because of n.

Rwater = 0.15.

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