If light of wavelength 690 nm is used in a double-slit experiment with slit separation 0.206 mm,what angle separates the two 4^th order maxima? A) 0.768$^{\circ}$ B) 3.07$^{\circ}$ C) 0.307$^{\circ}$ D) 1.54$^{\circ}$ E) 0.154$^{\circ}$

Question

Quizplus · Accepted Answer

The angle between the central maximum and the mth order maximum in a double-slit experiment can be calculated using the formula:
θ = mλ/d
where θ is the angle, λ is the wavelength of light, and d is the slit separation.
For the 4th and 5th order maxima (m=4,5), we have:
θ = 4λ/d and θ = 5λ/d
The angle between these maxima is the difference between the two angles:
Δθ = 5λ/d - 4λ/d = λ/d
Substituting the values given in the question, we get:
Δθ = (690 nm)/(0.206 mm) = 0.00354 radians
We can convert this to degrees:
Δθ = 0.00354 radians * (180/π) = 0.203 degrees
Therefore, the angle separating the two 4th and 5th order maxima is approximately 0.203 degrees, which is closest to option D) 1.54 degrees (rounded to two decimal places).

If Light of Wavelength 690 Nm Is Used in a Double-Slit