White light is passed through a double slit and interference is o… - Vidyadip

MCQ

White light is passed through a double slit and interference is observed on a screen $1.5 \,{m}$ away. The separation between the slits is $0.3 \,{mm}$. The first violet and red fringes are formed $2.0 \,{mm}$ and $3.5\, {mm}$ away from the central white fringes. The difference in wavelengths of red and voilet light is $.... \,{nm} .$

A
$150$
B
$1300$
✓
$300$
D
$600$

✓

Answer

Correct option: C.

$300$

c
Position of bright fringe ${y}={n} \frac{{D} \lambda}{{d}}$

${y}_{1} \text { of red }=\frac{{D} \lambda_{{r}}}{{d}}=3.5\, {mm}$

$\lambda_{{T}}=3.5 \times 10^{-3} \frac{{d}}{{D}}$

Similarly $\lambda_{{v}}=2 \times 10^{-3} \frac{{d}}{{D}}$

$\lambda_{{r}}-\lambda_{{v}}=\left(1.5 \times 10^{-3}\right)\left(\frac{0.3 \times 10^{-3}}{1.5}\right)$

$=3 \times 10^{-1}=300\, {nm}$

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