The figure below shows the standard setup for Young\'s double-slit experiment. T

Question

The figure below shows the standard setup for Young's double-slit experiment. The spacing between the slits is d, and the screen is a distance L away from the slits. The derivation of the two-slit interference conditions assumes that the two lines of sight to a point P are parallel, since L >> d, allowing us to approximate the path length difference as ?l =  dsin?. How good is this approximation? Suppose that L = 1.00 cm, d = 0.780 mm, and ? = 12.00°. (Under normal experimental conditions, L/d would be much larger than this, but we want to test the approximation for a case where L is closer to d.)

Use geometry and trigonometry to compute the value for the actual path length difference ?l. Enter your answer as a positive value.
0.1621 mm

You are correct.
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Explanation / Answer

Approximate l = d*sin120 = 0.780*0.2079 = 0.162171118

percantage =  ( Approximate_l - l )*100 / Approximate  l = (0.162171118 - 0.1621)*100/0.162171118 = 0.043853

So you can try 0.043853 or 0.04385 or 0.0439

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