Youngs Double Slit Experiment

To find the angular separation of the first-order bright fringe in a double-slit experiment, we proceed as follows:

Use the formula for the angular position of the $m$ -th bright fringe: $%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7Bm%20%5Clambda%7D%7Bd%7D.$
For the first-order fringe, set $m%20%3D%201$ .
Given: wavelength $%5Clambda%20%3D%20600%20%5C%2C%20%5Ctext%7Bnm%7D$ , slit separation $d%20%3D%200.2%20%5C%2C%20%5Ctext%7Bmm%7D$ .
Convert units to meters for consistency: $%5Clambda%20%3D%20600%20%5C%2C%20%5Ctext%7Bnm%7D%20%3D%20600%20%5Ctimes%2010%5E%7B-9%7D%20%5C%2C%20%5Ctext%7Bm%7D%20%3D%206%20%5Ctimes%2010%5E%7B-7%7D%20%5C%2C%20%5Ctext%7Bm%7D%2C$ $d%20%3D%200.2%20%5C%2C%20%5Ctext%7Bmm%7D%20%3D%200.2%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bm%7D%20%3D%202%20%5Ctimes%2010%5E%7B-4%7D%20%5C%2C%20%5Ctext%7Bm%7D.$
Calculate $%5Csin%20%5Ctheta$ : $%5Csin%20%5Ctheta%20%3D%20%5Cfrac%7B1%20%5Ctimes%206%20%5Ctimes%2010%5E%7B-7%7D%7D%7B2%20%5Ctimes%2010%5E%7B-4%7D%7D%20%3D%203%20%5Ctimes%2010%5E%7B-3%7D.$
For small angles, use the approximation $%5Csin%20%5Ctheta%20%5Capprox%20%5Ctheta$ (in radians), so: $%5Ctheta%20%5Capprox%203%20%5Ctimes%2010%5E%7B-3%7D%20%5C%2C%20%5Ctext%7Bradians%7D.$
Convert radians to degrees: $%5Ctheta_%7B%5Ctext%7Bdegrees%7D%7D%20%3D%203%20%5Ctimes%2010%5E%7B-3%7D%20%5Ctimes%20%5Cfrac%7B180%7D%7B%5Cpi%7D%20%5Capprox%203%20%5Ctimes%2010%5E%7B-3%7D%20%5Ctimes%2057.296%20%5Capprox%200.1719%5E%5Ccirc.$
Compare with options: 0.1719° is rounded to 0.172°.

Thus, the correct answer is: $%5Cboxed%7B0.172%5E%5Ccirc%7D$

Chapter Questions
1 MCQs