Question

The diagram shows rays of light from a point source, P, that reach a detector, D, along two paths. One path is a straight line, while the other is bent by reflection off a mirror. What is the value of b, correct to one decimal place? Assume that all the points in the diagram lie in the same plane.

5.4

4.2

3.6

2.8

Answer 1

Hello there.

The diagram shows rays of light from a point source, P, that reach a detector, D, along two paths. One path is a straight line, while the other is bent by reflection off a mirror. What is the value of b, correct to one decimal place? Assume that all the points in the diagram lie in the same plane.

3.6

Answer 2

This can solved using the cosine law which is:
c² = a² + b² - 2ab cos θ
Using the values given from the problem
6² = b² + b² - 2bb cos 112.62
And solving for b
36 = 2b² - 2b² cos 112.62
b = 3.6

The answer is the 3rd option.