1)A point source of light is located 4.5 m below the surface of a large pool of

Question

1)A point source of light is located 4.5 m below the surface of a large pool of water. Find the area of the largest circle on the pool's surface through which light coming directly from the source can emerge. m2

2)Two polarizing sheets have their transmission axes crossed so that no light gets through. A third sheet is inserted between the first two so that its transmission axis makes an angle ? with the transmission axis of the first sheet. Unpolarized light of intensity I0 is incident on the first sheet. Suppose that the middle sheet is replaced by two polarizing sheets. The angles between the transmission axes of the second, third and fourth sheets in the stack make angles of 30

Explanation / Answer

1.)

n1*sin(theta) = n2*sin(90)

(4/3)*sin(theta) = 1*1

So sin(theta) = 3/4

So theta = 48.6 degrees

r = d/tan(90-theta) = 4.5/tan(90-48.6) = 5.1 m

So Area = pi*r^2 = pi*(5.1)^2 = 81.8 m^2

2.) I4 = (I0/2)*cos^2(theta2-theta1)*cos^2(theta3-theta2)*cos^2(theta4-theta3)

= (I0/2)*cos^2(30-0)*cos^2(60-30)*cos^(90-60)

= (I0/2)*cos^2(30)*cos^2(30)*cos^(30)

= (I0/2)*cos^6(30)

= (27/128)*I0

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