A screen is placed 50cm away from a slit lit by a monochromatic light of wavelength 690nm. The distance seperating the first dark fringe and the third dark fringe in the diffraction pattern is 3mm. Calculate the width of the slit.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html

Well, you have y1-y2 as 3mm
and m1+1=m2

so in the two equations for the dark minimus, subtract one from the other to end with one equation using your indicie and the 3mm.

To calculate the width of the slit, we need to use the formula for the fringe spacing in a single-slit diffraction pattern. The formula is:

D * λ = w * L

Where:
- D is the distance between the adjacent dark fringes
- λ is the wavelength of the light
- w is the width of the slit
- L is the distance between the slit and the screen

We are given that the distance separating the first dark fringe and the third dark fringe (D) is 3 mm, which is equal to 0.3 cm. The wavelength of the light (λ) is 690 nm, which is equal to 6.9 x 10^-5 cm. The distance between the slit and the screen (L) is 50 cm.

Plugging in the given values into the formula, we have:

0.3 cm * (6.9 x 10^-5 cm) = w * (50 cm)

Simplifying the equation, we get:

w = (0.3 cm * (6.9 x 10^-5 cm)) / (50 cm)

Calculating the equation, we find:

w ≈ 4.14 x 10^-6 cm

So, the width of the slit is approximately 4.14 x 10^-6 cm.