Can you please explain how to solve this question? Would I need to use the formula nλ=dsin(theta)?

Red light with a wavelength of 660 nm and blue light with a wavelength of 480 nm are beamed at a double slit with a separation of 2x10^-3 mm. The third order maximums for the different colours occur at different spots. What is the angle between the second order maximums?

To solve this question, you would indeed need to use the formula nλ = d*sin(theta), which is known as the double-slit interference formula. This formula relates the wavelength (λ) of a wave, the distance between the two slits (d), the angle of the maximum (theta), and the order of the maximum (n).

Let's go step by step to solve the problem:

Step 1: Determine the given values:
- Red light wavelength (λ) = 660 nm = 660 × 10^-9 m
- Blue light wavelength (λ) = 480 nm = 480 × 10^-9 m
- Separation between the double slits (d) = 2 × 10^-3 mm = 2 × 10^-6 m

Step 2: Calculate the angles for the third order maximum:
To find the angle theta for the third order maximum, we need to use the formula nλ = d*sin(theta) and rearrange it as:
theta = sin^(-1)(nλ / d)

For red light:
- n = 3, λ = 660 × 10^-9 m, d = 2 × 10^-6 m

theta_red = sin^(-1)((3 * 660 × 10^-9 m) / (2 × 10^-6 m))

For blue light:
- n = 3, λ = 480 × 10^-9 m, d = 2 × 10^-6 m

theta_blue = sin^(-1)((3 * 480 × 10^-9 m) / (2 × 10^-6 m))

Step 3: Calculate the angle between the second order maximums:
To find the angle between the second order maximums, we need to subtract the angles of the third order maximums. Therefore:
angle_difference = |theta_red - theta_blue|

Keep in mind that we take the absolute value (| |) to ensure a positive difference.

Finally, you will have the angle between the second order maximums (angle_difference) as the result.

Remember to use a scientific calculator or an online calculator for the trigonometric calculations.