unpolarised light travels through two polarising filters X and Y and is then incident on a screen. When X and Y are arranged as shown, there is a maximum intensity on the screen. X is held stationary but Y is rotated in a plane at right angles to the beam so that θ increases. What are the next three values of θ, in rad, for which the beam hits the screen with maximum intensity?
Question
unpolarised light travels through two polarising filters X and Y and is then incident on a screen. When X and Y are arranged as shown, there is a maximum intensity on the screen. X is held stationary but Y is rotated in a plane at right angles to the beam so that θ increases. What are the next three values of θ, in rad, for which the beam hits the screen with maximum intensity?
Solution
The intensity of light after passing through a polarizer is given by Malus's law, which states that the intensity I of the transmitted light is directly proportional to the square of the cosine of the angle θ between the transmission axis of the polarizer and the direction of the incident light.
When the light is at maximum intensity, the angle θ is a multiple of π radians (or 180 degrees). This is because the cosine of multiples of π is either 1 or -1, and squaring these values gives a maximum intensity of 1.
Given that the light is initially at maximum intensity, we can assume that the initial angle θ is a multiple of π. As Y is rotated and θ increases, the next three values of θ for which the light will be at maximum intensity will be when θ is increased by π each time.
So, if we denote the initial angle as nπ (where n is an integer), the next three values of θ for maximum intensity will be (n+1)π, (n+2)π, and (n+3)π radians.
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