HELP WITH B !! The wings of some beetles have closely spaced parallel lines of m

Question

HELP WITH B !!

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.

Part A

If the melanin lines on the wing are spaced 2.0 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.

This is correct 16 degrees

Part B

If the vertical distance between your eyes and the beetle is 80 cm , 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.

Express your answer using three significant figures.

Explanation / Answer

Given
the angle theta is 16 degrees
and
the wavelength of the green light is 550 nm

we have the relation as

       Tan theta = y/R

where y is pependicular distance 0.8 m , then R = y/tan theta

                       R = 0.8/tan(16) = 2.79 m

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