Calculating Slit Width and Angular Deflection for 630nm and 450nm Light

[RachelSSS]

Light of wavelenght 630nm passes through a single slit. The angular deflection to the tenth dark band on the side of the center maximum is 3.6 degrees. A) Calculate the slit width. B) Calculate the angular deflection to the tenth dark band using light of 450 nm wavelenght.

Relevent Equations :

delta y = L(Lamda) over d.

 

[rl.bhat]

Convert degree into radian. Then angle theta = delta y/L = Lamda/d

 

[ogb p]

A) To calculate the slit width, we can use the equation delta y = L(Lamda) over d, where delta y is the angular deflection, L is the distance from the slit to the screen, Lamda is the wavelength of light, and d is the slit width. Rearranging the equation to solve for d, we get d = L(Lamda) over delta y. Plugging in the given values, we get d = L(630nm) over 3.6 degrees = 175nm. Therefore, the slit width is 175nm.

B) To calculate the angular deflection for 450nm light, we can use the same equation, but with a different wavelength. Plugging in the values, we get delta y = L(450nm) over 175nm = 2.57 degrees. Therefore, the angular deflection for the tenth dark band using 450nm light is 2.57 degrees. This shows that as the wavelength decreases, the angular deflection also decreases, indicating a narrower diffraction pattern. This is in accordance with the diffraction grating equation, which states that the angular deflection is inversely proportional to the wavelength.