The fringe width at a distance of 50cm from the slits in Yong's experiment for light of wavelength 6000Angstrom is 0.048cm.find the fringe wide at the same distance for wavelength=5000Angstrom?
We can use the formula for fringe width:
w = λD / d
where w 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 slits.
We are given that D = 50 cm, λ1 = 6000 Å, w1 = 0.048 cm, and we want to find λ2 and w2.
First, we can solve for d using the given values:
w1 = λ1D / d
d = λ1D / w1
d = (6000 Å) (50 cm) / (0.048 cm)
d ≈ 6.25 x 10^6 Å
Now we can plug in the values for λ2 and solve for w2:
w2 = λ2D / d
w2 = (5000 Å) (50 cm) / (6.25 x 10^6 Å)
w2 ≈ 0.04 cm
Therefore, the fringe width at a distance of 50 cm from the slits for light of wavelength 5000 Å is approximately 0.04 cm.
To find the fringe width at the distance of 50 cm for a different wavelength, we can use the formula:
δy = (λ * D) / d
Where:
δy is the fringe width,
λ is the wavelength of light,
D is the distance between the slits and the screen,
d is the distance between the centers of adjacent fringes.
Given that the wavelength for the first situation is 6000 Angstrom and the fringe width is 0.048 cm, we can calculate the distance between the slits and the screen (D) using the given fringe width:
D = (δy * d) / λ
Substituting the values into the equation, we get:
D = (0.048 cm * d) / 6000 Angstrom
Now, we can find the distance between the slits and the screen for the second wavelength (λ = 5000 Angstrom) using the same formula:
D' = (0.048 cm * d) / 5000 Angstrom
Therefore, the fringe width for the second wavelength at the same distance of 50 cm is equal to:
δy' = (λ' * D') / d = (5000 Angstrom * D') / d
Now we need to substitute the value of D' and rearrange the formula:
δy' = [(5000 Angstrom * (0.048 cm * d) / 5000 Angstrom)] / d
Simplifying the equation:
δy' = 0.048 cm
Hence, the fringe width at a distance of 50 cm for a wavelength of 5000 Angstrom is also 0.048 cm.