Question

a glass prism in the shape of a quarter-cylinder lies on a horizontal table.a uniform, horizontal light beam falls on its vertical plane surface, as shown in the figure. if the radius of the cylinder is R=5cm and the refractive index of the glass is n=1.5,where , on the table beyond the cylinder, will a path of light be found?

Answer 1

a glass prism in the shape of a quarter-cylinder lies on a horizontal table. a uniform, horizontal light beam falls on its vertical plane surface, as shown in the figure. if the radius of the cylinder is $R = 5\mathrm{cm}$ and the refractive index of the glass is $n = 1.5$ , where, on the table beyond the cylinder, will a path of light be found?

Solution

Referring to the ray diagram, we have, $\sin \theta c = \frac{1}{n}$ and

$$\cos \theta c = \frac {R}{R + x}, \cos \theta c = \sqrt {1 - (\sin \theta c) ^ {2}} = \sqrt {1 - \frac {1}{n ^ {2}}} = \sqrt {1 - \frac {1}{1 . 5 ^ {2}}} = 0. 7 4 5$$

giving $x = R\left(\frac{1}{0.745} - 1\right) = 5\left(\frac{1}{0.745} - 1\right) = 1.71 \, \text{cm}$ .

Now consider the lower part of the cylinder as a planoconvex lens to get $f = 2R = 10 \, \text{cm}$ . Thus the path of light will be found between $1.71 \, \text{cm}$ and $10 \, \text{cm}$ beyond the cylinder.

Answer: between 1.71 cm and 10 cm beyond the cylinder.