Question

Light with a wavelength of 7.2 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

1.09 x 10-5 m

9.66 x 10-6 m

7.63 x 10-6 m

5.44 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 the bright fringes given by:

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

where:
- \(y_m\) is the distance from the central maximum to the m-th order maximum (in this case, \(y_1\) for the first order),
- \(m\) is the order of the maximum (1 for the first order),
- \(\lambda\) is the wavelength of the light,
- \(L\) is the distance from the slits to the screen,
- \(d\) is the separation between the slits.

Given:
- \(\lambda = 7.2 \times 10^{-7} \, \text{m}\)
- \(L = 1.00 \, \text{m}\)
- \(y_1 = 0.0655 \, \text{m}\)

We need to find \(d\). Rearranging the formula, we get:

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

Now, substituting in the values for the first order (where \(m = 1\)):

\[
d = \frac{1 \cdot (7.2 \times 10^{-7}) \cdot (1.00)}{0.0655}
\]

Calculating the numerator:

\[
d = \frac{7.2 \times 10^{-7}}{0.0655}
\]

Now calculating that value:

\[
d \approx \frac{7.2 \times 10^{-7}}{0.0655} \approx 1.097 \times 10^{-5} \, \text{m}
\]

Now rounding it to two decimal places:

\[
d \approx 1.09 \times 10^{-5} \, \text{m}
\]

Thus, the separation between the slits is

\[
\boxed{1.09 \times 10^{-5} \, \text{m}}
\]