Question

In YDSE, d is the distance between slits and $D$ is the distance between screen and slit plane. If $y_1$ is the distance of $1^{st}$ maxima from the central maxima for red light and $y^2$ is the distance for violet light then what is the difference between the wavelength of red and violet?

• A. $\frac{(y_1+y_2)d}{D}$
• B. $\frac{(y_1-y_2)d}{D}$
• C. $\frac{(y_1-y_2)D}{d}$
• D. $\frac{(y_1+y_2)D}{d}$

Answer 1

The correct option is B

$\frac{(y_1-y_2)d}{D}$

Solution:

Step 1: Given information

Distance between screen and slit plane$=D$

The distance of $1^{st}$ maxima for red light = $y_1$

The distance for violet light = $y_2$

Step 2: Draw the required diagram

Draw the required figure:

From the condition of maximum:

$y_1=\frac{{\lambda }_{r}D}{d}$….(i)

$y_2=\frac{{\lambda }_{u}D}{d}$….(ii)

Step 3: Calculate the difference between the wavelength of red and violet

Subtract equation (ii) from equation (i):

$\begin{array}{l}\Rightarrow y_1-y_2=\frac{{\lambda }_{r}D}{d}-\frac{{\lambda }_{u}D}{d}\\ \Rightarrow y_1-y_2=\frac{\left({\lambda }_r-{\lambda }_u\right)D}{d}\\ \Rightarrow {\lambda }_r-{\lambda }_u=\frac{\left(y_1-y_2\right)d}{D}\end{array}$

Hence, the correct option is (B).