Question

A white light is incident at ${20}^{\circ }$ on a material of silicate flint glass slab as shown. ${\mu }_{violet}=1.66$ and ${\mu }_r=1.6$ . For what value of $d$ will separation be $1mm$ in red and violet rays?

• A. $\frac{10}{3}cm$
• B. $\frac{20}{3}cm$
• C. $\frac{5}{3}cm$
• D. $5cm$

Answer 1

Answer: (A)

Here, glancing angle is given ${20}^{\circ }$

Therefore, angle of incidence is : ${90}^{\circ }-{20}^{\circ }={70}^{\circ }$

$\sin r_v=\frac{\sin {70}^{\circ }}{1.66}=\frac{0.9397}{1.66}or{r}_v={34}^{\circ }{30}^{{}^{\prime }}\sin r_r=\frac{\sin {70}^{\circ }}{1.6}=\frac{0.9397}{1.6}or{r}_r={36}^{\circ }$

Using $l=\frac{t\sin (i-r)}{\cos r}{l}_v-l_r=d[\frac{\sin (i-r_v)}{cos{r}_v}-\frac{\sin (i-r_r)}{cos{r}_r}]0.1=d[\frac{\sin {35}^{\circ }{30}^{{}^{\prime }}}{cos{34}^{\circ }{30}^{{}^{\prime }}}-\frac{\sin {34}^{\circ }}{cos{36}^{\circ }}]or0.1=d[\frac{0.5807}{0.8241}-\frac{0.5592}{0.8090}]=d[0.71-0.68]ord=\frac{0.1}{0.03}=\frac{10}{3}cm$