A ray of sunlight hits a frozen lake at a 45° angle of incidence. At what angle of refraction does the ray penetrate the ice? At what angle does it penetrate the water beneath the ice?

1 Answer
Dec 19, 2016

Answer:

Angle of refraction at the air-ice interface#=32.7^@#
Angle of refraction at the ice-water interface#=32.1^@#

Explanation:

Using the following refractive indices
Air #=1.00#
Water#=1.33#
Ice #=1.31#

Using Snell's Law of refraction applicable for a ray crossing the interface between two media which have refractive indices #n_1# and #n_2# as shown in the figure.

wikipedia

#n_1 sinθ_1 = n_2 sinθ_2#
where #θ_1 and θ_2# are the angles of incidence and refraction respectively.

For first interface when ray enters from air to ice
#1.00xxsin 45 = 1.31xxsin theta_2#
#=>sin theta_2 =(sin 45/1.31)= 0.5398#, rounded to four decimal places
#=>theta_2 =sin^-1(0.5398)=32.7^@#, rounded to one decimal place.

Due to geometry this becomes angle of incidence for the second interface as ray enters from ice to water. Using Snell's law again we have

#1.31xxsin 32.67 = 1.33 xxsin theta_2#
#theta_2 = sin^-1((1.31xx0.5398)/1.33)=32.1^@#, rounded to one decimal place