Exploring Dark Fringes: How Many Dark Fringes Will Be Produced?
How many whole dark fringes will be produced on an infinitely large screen if blue light (λ = 475 nm) is incident on two slits that are 20.0 μm apart?
To find the number of dark fringes, we need to determine the angular separation between them. How can we calculate this?
Answer:
The number of whole dark fringes on an infinitely large screen can be calculated by considering the angular separation between them. The dark fringes occur at angles that satisfy the condition:
Dark fringes occur at angles that satisfy the following condition: sin(θ) = (m + 1/2) * λ / d
Where:
- θ is the angle between the central maximum and the m-th dark fringe
- m is an integer (0, 1, 2, ...)
- λ is the wavelength of the light (475 nm)
- d is the distance between the two slits (20.0 μm)
Given the values of λ = 475 nm and d = 20.0 μm, we can calculate the angular separation between the dark fringes using the formula:
sin(θ) = (m + 1/2) * (475 * 10^-9 m) / (20.0 * 10^-6 m)
By considering the range of angles from -90° to 90°, we can determine the number of whole dark fringes. The calculated values for m_min and m_max are:
m_min ≈ -20
m_max ≈ 20
Therefore, the total number of whole dark fringes within this range is 41. Hence, there will be 41 whole dark fringes on an infinitely large screen with blue light incident on two slits.