Join WhatsApp Icon JEE WhatsApp Group
Question 26

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is 6600 $$\text{Å}$$, then wavelength of first maximum will be:

In a single slit diffraction experiment, the position of minima and maxima are determined by specific conditions. For the first minimum of red light, the condition is given by:

$$ a \sin \theta = n \lambda $$

where $$ a $$ is the slit width, $$ \theta $$ is the angle from the central maximum, $$ \lambda $$ is the wavelength, and $$ n $$ is the order of the minimum. For the first minimum, $$ n = 1 $$. Given the wavelength of red light $$ \lambda_r = 6600 \text{Å} $$, we have:

$$ a \sin \theta = 1 \cdot 6600 = 6600 \text{Å} \quad \text{(Equation 1)} $$

For the first maximum of another light with wavelength $$ \lambda $$, the condition is approximately:

$$ a \sin \theta = \left( m + \frac{1}{2} \right) \lambda $$

where $$ m $$ is the order of the maximum. For the first maximum, $$ m = 1 $$, so:

$$ a \sin \theta = \left( 1 + \frac{1}{2} \right) \lambda = \frac{3}{2} \lambda \quad \text{(Equation 2)} $$

The problem states that the first minimum for red light coincides with the first maximum of the other light. This means the angular position $$ \theta $$ is the same for both, so $$ \sin \theta $$ is identical. Therefore, the expressions for $$ a \sin \theta $$ from Equation 1 and Equation 2 must be equal:

$$ 6600 = \frac{3}{2} \lambda $$

Solving for $$ \lambda $$:

$$ \lambda = 6600 \times \frac{2}{3} $$

Performing the multiplication:

$$ \lambda = \frac{6600 \times 2}{3} = \frac{13200}{3} = 4400 \text{Å} $$

Thus, the wavelength of the other light for which the first maximum coincides with the first minimum of red light is 4400 Å.

Comparing with the options:

A. 3300 Å

B. 4400 Å

C. 5500 Å

D. 6600 Å

Hence, the correct answer is Option B.

Get AI Help

Create a FREE account and get:

  • Free JEE Mains Previous Papers PDF
  • Take JEE Mains paper tests

50,000+ JEE Students Trusted Our Score Calculator

Predict your JEE Main percentile, rank & performance in seconds

Ask AI

Ask our AI anything

AI can make mistakes. Please verify important information.