Question

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping intererence patterns on the screen. The central maximum of both lights coincides.

Further, it is observed that the third bright fringe of known light coincides with the 4^th bright fringe of the unknown light. From this data the wavelength of the unknown light is ______.

Options

• 885.0 nm

• 442.5 nm

• 776.8 nm

• 393.4 nm

Answer 1

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping intererence patterns on the screen. The central maximum of both lights coincides.

Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data the wavelength of the unknown light is 442.5 nm.

Explanation:

We know that n^th maxima occurs at a distance `("n"λ"D​")/"d"` from the central maxima.

For the known light, 3^rd maxima will occur at a distance `(3xx590xx"D")/"d"xx10^-9`m from the central maxima.

For the unknown wavelength λ, the 4^th maxima will occur at a distance `(4λ"D")/"d"`​ from the central maxima.

If both coincide, `(3xx590xx"D")/"d"xx10^-9"m"=(4lambda"D")/"d"`

Solving this, we get λ = 442.5nm