The fringe width at a distance of 50cm from the slits in Young's experiment for light of wavelength 6000Angstrom is 0.048cm. Find the fringe width at the same distance for wavelength=5000aAngstrom?
We can use the formula for fringe width in Young's double slit experiment:
β = λD/d
where β is the fringe width, λ is the wavelength of light, D is the distance from the slits to the screen, and d is the distance between the two slits.
Given:
λ1 = 6000 Å
λ2 = 5000 Å
D = 50 cm
β1 = 0.048 cm
Using the formula for β1, we can find d1:
d1 = λ1D/β1 = (6000 Å) (50 cm) / (0.048 cm) = 6.25 x 10^6 Å = 0.625 mm
Now we can use d1 to find β2:
β2 = λ2D/d1 = (5000 Å) (50 cm) / (0.625 mm) = 0.4 cm
Therefore, the fringe width at a distance of 50 cm from the slits for light of wavelength 5000 Å is 0.4 cm.
To find the fringe width at a distance of 50 cm for a different wavelength in Young's experiment, you can use the formula:
Fringe width (W) = (wavelength * distance) / distance between slits
Given:
- Wavelength 1 (λ1) = 6000 Angstrom
- Fringe width at a distance of 50 cm for λ1 (W1) = 0.048 cm
- Wavelength 2 (λ2) = 5000 Angstrom
Let's calculate the distance between slits (d) first, using the given fringe width for λ1:
W1 = (λ1 * 50 cm) / d
Solving for d:
d = (λ1 * 50 cm) / W1
Now, we can plug in the values to find the distance between slits:
d = (6000 Angstrom * 50 cm) / 0.048 cm
d = 6250000 Angstrom-cm
Next, we can use the calculated slits distance (d) and the given wavelength (λ2) to find the fringe width (W2) for λ2:
W2 = (λ2 * 50 cm) / d
W2 = (5000 Angstrom * 50 cm) / 6250000 Angstrom-cm
Simplifying the equation:
W2 = 250000 Angstrom-cm / 6250000 Angstrom-cm
W2 = 0.04 cm
Therefore, the fringe width at a distance of 50 cm for a wavelength of 5000 Angstrom is 0.04 cm.