4. A light wave of yellow sodium light (? = 5.89 × 10^-7m) in air is incident on

Question

4. A light wave of yellow sodium light (? = 5.89 × 10^-7m) in air is incident on a
?at pool of an unknown transparent liquid, at an angle of 60? with the normal.
The speed of light in this liquid is known to be 2.01 × 10^8m/s .

a) What angle does the refracted wave make the normal?

b) What angle does the re?ected wave make with the normal?

c) What might the unknown liquid be? Explain how you decided this.

d) What is the critical angle for this light wave exiting out the bottom of this
pool of liquid back into the air?

Explanation / Answer

Wavelength of yellow light = 5.89 x 10 -7 m Angle of incidence i = 60 o Speed of light in the liquid v = 2 .01 x 10 8 m / s (a). Index of refraction of liquid n = c / v Where c = Speed of the in vaacum                = 3 x 10 8 m / s So, n = 1.492 Index of refraction of air n ' = 1 From Snell's law sin i / sin r = n '/ n                                            = 1.492                                                                                 sin r = sin i /1.492                                            = 0.58                                          r = 35.46 o (b). Angle of reflection r ' = i                                         = 60 o (c). The liquid is sogar solution. (d). Critical angle C = ? We know sin C = 1/ n                           = 0.67                        C = 42.06 o

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