A student studies a beam of light that comes from a lamp and a polarising filter together…

A student studies a beam of light that comes from a lamp and a polarising filter together. The beam is a mixture of two parts. The unpolarised part has an intensity of $36\ \text{W/m}^2$, and the plane polarised part has an intensity of $84\ \text{W/m}^2$. She puts an analyser in the beam and turns it slowly through half a circle, and a light meter behind the analyser records the intensity. The light meter has been checked, and it reads the intensity in watt for each square metre. She writes down the readings at many angles, and she wants to know the highest and the lowest values, and how strongly the beam is polarised. She measures the angle of the analyser from the direction of vibration of the polarised part. Find the greatest and the least intensity that she records, and the degree of polarisation of the beam. Find also the intensity at $30^\circ$ and the angle at which the intensity is $60\ \text{W/m}^2$.