In a single slit diffraction experiment first minima for λ₁ = 660 n m coincides with first maxima for wavelength λ₂. Calculate the value of λ₂.

In a single slit diffraction experiment, the condition for the first minima is given by the formula:

Minima Condition

The position of the first minima can be expressed as:

• a sin(θ) = λ

Here, a is the width of the slit, θ is the angle of diffraction, and λ is the wavelength of light.

Maxima Condition

For the first maxima, the condition is slightly different:

• a sin(θ) = 2λ/3

Given Conditions

In this scenario, the first minima for wavelength λ₁ = 660 nm coincides with the first maxima for wavelength λ₂.

Setting Up the Equation

Since both conditions occur at the same angle θ, we can set the two equations equal to each other:

• λ₁ = 2λ₂/3

Calculating λ₂

Now, substituting the value of λ₁:

• 660 nm = 2λ₂/3

To find λ₂, rearrange the equation:

• λ₂ = (660 nm * 3) / 2

Calculating this gives:

• λ₂ = 990 nm

Final Result

The value of λ₂ is 990 nm.