Why is the following situation impossible? The perpendicular distance of a light

Question

Why is the following situation impossible? The perpendicular distance of a light bulb from a large plane mirror is twice the perpendicular distance of a person from the mirror. Light from the light bulb reaches the person by two paths: (1) it travels to the mirror and reflects from the mirror to the person, and (2) it travels directly to the person without reflecting off the mirror. The total distance traveled by the light in the first case is 3.10 times the distance traveled by the light in the second case. The light beam in Figure P25.53 strikes surface 2 at the critical angle. Determine the angle of incidence theta_1, . A light ray of wavelength 589 nm is incident at an angle theta on the top surface of a block of polystyrene as shown in Figure P25.54. (a) Find the maximum value of theta for which the refracted ray undergoes total internal reflection at the point P located at the left vertical face of the block. What If? Repeat the calculation for the case in which the polystyrene block is immersed in (b) water and (c) carbon disulfide. Explain your answers. A transparent cylinder of radius R = 2.00 m has a mirrored surface on its right half as shown in Figure P25.55. A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and exiting light ray are parallel

Explanation / Answer

from the figure

angle of refraction

theta ( r) = 90 - ( 180 -60-48 )

theta (r) = 18 degree

since 42 degree is critical angle

u = 1/sin42 = 1.49

we have from snelts law

1x sin theta = u sin theta (r)

theta ( i) = 27.5 degree

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