(a) A tank containing methanol has walls 2.50 cm thick made of glass of refracti

Question

(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.570. Light from the outside air strikes the glass at a 43.1° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (The index of refraction of methanol is 1.329.)
°

(b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?

Explanation / Answer

PART A Frome snells laws

n1*sintheta1 = n2*sintheta2

n1 = refractive index of medium 1

theta1 is the angle(incident) made by the light ray with the normal in medium 1.

n2 = refractive index of medium 2

theta2 is the angle(refracted) made by the light ray with the normal in medium 2 from air to glass

nair*sintheta1 = n_glass*sintheta2

1*sin43.1 = 1.570*sintheta2........(1)

From glass to methanol

n_glass*sintheta2 = n_meth*sintheta3

From 1

sin43.1 = n_meth*sintheta3

sin43.1 = 1.329*sintheta3......(2)

theta3 = 30.94 degrees

PART B

Here theta1 = 43.1 and theta3 = 20.2

From 1

1*sin43.1 = n_lq*sin20.2

n_lq = 1.978

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