Question

*To measure the index of refraction u of a liquid with an Abbe refractometer, a drop is placed between two prisms and a mirror is rotated until the boundary of the light and dark zones align with the crosshairs in a microscope. The index of refraction of the liquid is given by the following equation in which the angle of rotation is 0 and u, is the refractive index of glass (1.51). For liquid A, the value of 0 was found to be 150°, and for B, it was 75º. Using a worksheet, find u for each liquid: v=ta [(: –sin?o)"? + sin o)

Answer 1

Given that angle of rotation is $\Theta$ and let n_g be the refractive index of glass.

1-For liquid A  $\Theta$=150° and n=1.51

n=1/$\sqrt{}$2((n_g²-sin²$\Theta$)^0.5+sin$\Theta$)

n=0.707((2.2801-sin²(150°)^0.5+sin(150°)

n =0.707((2.2801-0.25)^0.5+0.5)

n =0.707*1.9248

n =1.36

2-For liquid B $\Theta$ =75° and n=1.51

n=1/$\sqrt{}$2((n_g²-sin²$\Theta$)^0.5+sin$\Theta$)

n=0.707((2.2801-sin²(75°)^0.5+sin(75°)

n=0.707((2.2801-0.927)^0.5+0.96)

n=0.707*2.12

n=1.501