A Fermat’s principle of least time for refraction. A ray of light traveling in a medium with speed leaves point A and strikes the boundary between the incident and transmitted media a horizontal distance x from point A as shown in Figure P38.98. The refracted ray travels with speed in the second medium, eventually reaching point B. The horizontal distance between points A and B is L.
a. Calculate the time t required for the light to travel from A to B in terms of the parameters labelled in the figure.
b. Now take the derivative of t with respect to x. What is the condition for which the ray of light will take the shortest time to travel from A to B?
5) A light ray incident on a block of glass makes an incident angle of 50.0° with the normal to the surface. The refracted ray in the block makes a 26.8° with the normal. What is the index of refraction of the glass?
6)
A light ray traveling from a higher index of refraction medium into a lower index of refraction medium (for example, from water into the air) would bend away from the normal to the medium surface. When the refracted ray is parallel to the boundary of the medium, θ2= 90°. The incident angle, θ1, becomes θc, called the
