In a Young's Double Slit experiment, the separation of four bright fringes is 2.5mm, the wavelength of light used is 6.2*10^-7m. If the distance from the slits to the screen is 80cm, calculate the separation of two slits.
I tried applying
4*¥D/d=1.5*10^-3m
But kept getting wrong answer. What's am I doing wrong?
You can't use 4*¥D/d=1.5*10^-3m for calculation of d because that formula is for distance between central bright fringe & 4rth bright fringe not for distance between four bright fringes.
In the Young's Double Slit experiment, the separation of two consecutive bright fringes is given by the formula:
Δy = λL / d
Where:
Δy is the separation between two consecutive bright fringes,
λ is the wavelength of light used,
L is the distance from the slits to the screen, and
d is the separation of the two slits.
You correctly set up the equation and plugged in the values:
4 * Δy = 1.5 * 10^-3 m
λ = 6.2 * 10^-7 m
L = 80 cm = 0.8 m
So, the equation becomes:
4 * (λL / d) = 1.5 * 10^-3 m
Now, let's rearrange the equation to solve for d:
d = λL / (4 * Δy)
Plugging in the values, we get:
d = (6.2 * 10^-7 m) * (0.8 m) / (4 * 2.5 * 10^-3 m)
Calculating this, we find:
d ≈ 0.0000992 m
So, the separation of the two slits is approximately 0.0000992 m, or 9.92 μm.
If you are getting a different answer, it could be due to errors in unit conversions or decimal calculations. Make sure to check your calculations and ensure all units are consistent. Also, watch out for any tiny mistakes, such as using the wrong exponent or not dividing correctly.
To calculate the separation of the two slits in a Young's Double Slit experiment, you'll need to use the formula:
λ = (m * λ * D) / d
Where:
λ is the wavelength of light used,
m is the order of the bright fringes,
D is the distance from the slits to the screen, and
d is the separation of the two slits.
In your case, you have the following values:
λ = 6.2 * 10^-7 m,
m (order of bright fringes) = 4, and
D (distance from the slits to the screen) = 80 cm = 0.8 m.
Using the formula, you can rearrange it to solve for d:
d = (m * λ * D) / λ
Plugging in the values:
d = (4 * 6.2 * 10^-7 * 0.8) / 6.2 * 10^-7
Calculating that, you should get:
d = 5.12 * 10^-3 m
Therefore, the separation of the two slits is 5.12 mm. Assuming you made a calculation error, double-check your calculations and the units.