The wings of some beetles have closely spaced parallel lines of melanin, causing

Question

The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing.

If the melanin lines on the wing are spaced 4.0?m apart, what is the first-order diffraction angle for green light (?  = 550 nm)? Note: The small-angle approximation will not work in this problem.

If the vertical distance between your eyes and the beetle is 30cm , how far away (in meters) should you stand in order to see the green light? Note: The small-angle approximation will not work in this problem.

Explanation / Answer

The condition of diffraction is

d sin ( theta ) = m ( lamda )

sin ( theta ) = ( 1) ( 550*10^ -9 m ) / ( 4.0*10^ -6 m )

theta = 7.9 degrees

The vertical distance between eyes and beetle is

Y = L tan ( theta )

L = ( 30 cm ) / tan 7.9

=216.19 cm

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