Questions: The first order maximum in a double slit experiment occurs at an angle of 10.0°. Calculate the slit separation if a 625 nm light source is used. (3.60 × 10^-6 m)

Solution Steps

In a double slit experiment, the condition for the first order maximum is given by the formula: \[ d \sin \theta = m \lambda \] where \( d \) is the slit separation, \( \theta \) is the angle of the maximum, \( m \) is the order of the maximum, and \( \lambda \) is the wavelength of the light.

From the problem, we know:

• \( \theta = 10.0^{\circ} \)
• \( \lambda = 625 \, \text{nm} = 625 \times 10^{-9} \, \text{m} \)
• \( m = 1 \) (first order maximum)

Rearrange the formula to solve for \( d \): \[ d = \frac{m \lambda}{\sin \theta} \] Substitute the known values into the equation: \[ d = \frac{1 \times 625 \times 10^{-9} \, \text{m}}{\sin 10.0^{\circ}} \]

Calculate \( \sin 10.0^{\circ} \) and then compute \( d \): \[ \sin 10.0^{\circ} \approx 0.1736 \] \[ d = \frac{625 \times 10^{-9}}{0.1736} \approx 3.60 \times 10^{-6} \, \text{m} \]

Final Answer