Laser light of wavelength 630 nm incident on a pair of slits produces an interference pattern in which the bright fringes are separated by 8.3 mm. A second light produces an interference pattern in which the bright fringes are separated by 7.6 mm. Find the wavelength of the second light.

To find the wavelength of the second light, we can use the formula for the fringe separation in a double-slit interference pattern:

Fringe Separation Formula

The formula is given by:

d = λL / s

• d = distance between fringes (separation)
• λ = wavelength of the light
• L = distance from the slits to the screen
• s = distance between the slits

Given Data

For the first light:

• Wavelength (λ₁) = 630 nm = 630 x 10^-9 m
• Fringe separation (d₁) = 8.3 mm = 8.3 x 10^-3 m

For the second light:

• Fringe separation (d₂) = 7.6 mm = 7.6 x 10^-3 m

Calculating the Wavelength of the Second Light

Since the distance from the slits to the screen (L) and the distance between the slits (s) remain constant for both lights, we can set up a ratio:

d₁ / λ₁ = d₂ / λ₂

Rearranging gives:

λ₂ = λ₁ * (d₂ / d₁)

Substituting the Values

Now, substituting the known values:

λ₂ = 630 x 10^-9 m * (7.6 x 10^-3 m / 8.3 x 10^-3 m)

Calculating this:

λ₂ ≈ 630 x 10^-9 m * 0.9157 ≈ 577.5 x 10^-9 m

Final Result

The wavelength of the second light is approximately 577.5 nm.