Refraction of Light Exercises (1) The wavelength of a laser beam in air is 488 n

Question

Refraction of Light Exercises (1) The wavelength of a laser beam in air is 488 nm. The beam is incident from air (n -1.00) onto a water surface. The angle of incidence is 48.5o and the angle of refraction in the water is 34.3 (a) What is the wavelength of the light in the water? (answer: 367 nm) (b) What is the energy per photon (in eV) in the air? What is the energy per photon (in eV) in the water? (answer: 2.55 ev in both water and air) (e) What color will the beam be perceived to have in air? What color will the beam be perceived to have in the water? (answer: bluish-green in both water and air) 488 nm) 2- C. (2) Refer to the glass paper weight shown below with index of refraction n-1.38: (a) Find the value of 0 for which the reflection at the vertical surface just satisfies the condition for total internal reflection. Use n-1.00 for air. (answer: 72.1°) (b) If the value of ? is increased above the value found in part (a), will there still be total internal reflection at the vertical surface? (answer: no, because the angle of incidence at the vertical surface will drop below the critical angle) n1.38

Explanation / Answer

1)

lambda_air=488 nm

n_air=1

n_water=1.33

theta1=48.5 degrees

theta2=34.3 degrees

a)

lambda_water=lambda_air/n_water

=488/1.33

=366.92 nm or 367 nm

b)

in the air,

energy per photon,

E=h*c/lambda_air

=6.626*10^-34*3*10^8/(488*10^-9)

=4.07*10^-19 J

=2.54 ev

and

in the water,

energy per photon,

E=h*c/lambda_water

=6.626*10^-34*3*10^8/(366.92*10^-9)

=5.417*10^-19 J

=3.38 ev

c)

the color of the light in VIBGYOR is

lambda_air=488nm ---> near blue

and

lambda_water=367nm ---> near violet

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