MCQ 11 Mark
An equi$-$convex crown glass lens has a focal length $20 \ cm$ for violet rays. Here $\mu_{ v }=1.5 \ \mu_{ r }=1.47$. Its focal length for red rays is
- A$24.85 \ cm$
- B$20.82 \ cm$
- ✓$21.28 \ cm$
- D$22.85 \ cm$
Answer
View full question & answer→Correct option: C.
$21.28 \ cm$
$\frac{1}{f}=\left(\frac{\mu_2}{\mu_1}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
For violet light,
$\frac{1}{f_v}=(1.5-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=0.5\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
For red light,
$\frac{1}{f_r}=(1.47-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=0.47\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
Hence, $f_r=\frac{0.5}{0.47} f_v$
$=1.064 \times 20$
$=21.28 \ cm$
For violet light,
$\frac{1}{f_v}=(1.5-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=0.5\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
For red light,
$\frac{1}{f_r}=(1.47-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)=0.47\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
Hence, $f_r=\frac{0.5}{0.47} f_v$
$=1.064 \times 20$
$=21.28 \ cm$


