Light of wavelength 5.2 × 10⁻⁷ m is used in a Young's double-slit experiment - AQA - A-Level Physics - Question 20 - 2022 - Paper 1

To find the separation (d) of the two slits in a double-slit experiment, we can use the formula for fringe width (β):

eta = \frac{\lambda L}{d}

where:

• (\beta) = fringe width,
• (\lambda) = wavelength of the light,
• (L) = distance from slits to screen,
• (d) = separation of the slits.

Given:

• (\lambda = 5.2 \times 10^{-7} \text{ m},)
• (L = 1.5 \text{ m},)
• width of ten fringes = 3.5 cm = 0.035 m. Therefore, the fringe width is:

$$\beta = \frac{0.035 \text{ m}}{10} = 0.0035 ext{ m}$$

Now, rearranging the fringe width formula to find d:

$$d = \frac{\lambda L}{\beta}$$

Substituting the known values:

$$d = \frac{(5.2 \times 10^{-7} \text{ m})(1.5 \text{ m})}{0.0035 \text{ m}} = 2.2 \times 10^{-4} \text{ m}$$

Thus, the separation of the two slits is approximately (2.2 \times 10^{-4} \text{ m}).