If a pinhole camera pointing vertically upwards is filled with a liquid and taken to an open space the image of the sky is found to be a circular disc of definite radius when the receiving screen is large enough . Explain this and deduce the refractive index of the liquid given that the perpendicular distance of the pinhole from the image is 10 cm and the radius of the image is 8 cm.(answer:1.6)
2007-05-05 04:06:07 · 1 answers · asked by kiyucheng 1 in Science & Mathematics ➔ Physics
From Snell's law (see ref.), N1*sin(theta1) = N2*sin(theta2), so N2 = N1*sin(theta1) / sin(theta2).
Define theta1 and N1 as pertaining to air, and N2 and theta2 to the liquid. Then N1 = 1. Set theta1 = the maximum angle of incidence of an external ray entering the camera = 90 deg. Then sin(theta1) = 1.
For the internal ray, given that the opposite side = 8 and the adjacent side = 10, the hypotenuse = sqrt(8^2+10^2) and sin(theta2) = 0.6247.
N2 = 1/sin(theta2) = 1.601.
2007-05-07 11:45:44 · answer #1 · answered by kirchwey 7 · 0⤊ 0⤋