Question

Light with a wavelength of 3.9 x 10-7 m is used in a double slit experiment. The screen is placed 1.00 m from the slits and the first order line is found 0.0655 m from the central bright spot. What is the separation between the slits?
Group of answer choices

7.63 x 10-6 m

5.95 x 10-6 m

4.66 x 10-6 m

9.66 x 10-6 m

Answer 1

To find the separation between the slits in a double-slit experiment, we can use the formula for the position of bright spots (fringes) on the screen:

\[
y_m = \frac{m \lambda L}{d}
\]

Where:
- \( y_m \) is the position of the m-th order bright spot from the central maximum,
- \( m \) is the order of the bright spot (for the first order, \( m = 1 \)),
- \( \lambda \) is the wavelength of the light,
- \( L \) is the distance from the slits to the screen,
- \( d \) is the separation between the slits.

From the problem:
- \( y_1 = 0.0655 \, \text{m} \) (first order fringe),
- \( \lambda = 3.9 \times 10^{-7} \, \text{m} \),
- \( L = 1.00 \, \text{m} \),
- \( m = 1 \).

Plugging in the values for the first-order bright spot:

\[
0.0655 = \frac{1 \cdot (3.9 \times 10^{-7}) \cdot 1.00}{d}
\]

Now we can solve for \( d \):

\[
d = \frac{(3.9 \times 10^{-7}) \cdot 1.00}{0.0655}
\]

Calculating this:

\[
d = \frac{3.9 \times 10^{-7}}{0.0655} \approx 5.95 \times 10^{-6} \, \text{m}
\]

Thus, the separation between the slits is approximately \( 5.95 \times 10^{-6} \, \text{m} \).

Therefore, the correct answer is:

**5.95 x 10-6 m**