1) The ceiling of your lecture hall is probably covered with acoustic tile, whic

Question

1) The ceiling of your lecture hall is probably covered with acoustic tile, which has small holes separated by about 6.3 mm. Using light with a wavelength of 598 nm, how far could you be from this tile and still resolve these holes? The diameter of your eye is about 5 mm.
_______m

Could you resolve these holes better with red light or with violet light? (choose one)
1. violet
2. red

2) A plano-convex glass lens of radius of curvature 2.5 m rests on an optically flat glass plate. The arrangement is illuminated from above with monochromatic light of 560-nm wavelength. The indexes of refraction of the lens and plate are 1.6. Determine the radii of the first and second bright fringes in the reflected light.

First bright fringe:
_________m

Second bright fringe:
_________m

watch units please, thank you!

Explanation / Answer

To clear up the question of whether red or violet light would be better to resolve the holes:

Red light: wavelength between 625nm and 750nm

Violet light: wavelength between 380nm and 450nm

Find L (or D whatever you want to call it for both cases)

Lr = [(5e-3)(6.3e-3)] / [(1.22)(625e-9)] = 41.311 m

Lv = [(5e-3)(6.3e-3)] / [(1.22)(380e-9)] = 67.947 m

Because you are able to resolve the holes from further away with violet light, you are able to resolve the holes better with violet light. Therefore the rule of thumb is that the shorter the wavelength, the higher the resolution/better ability to resolve.

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