Light of a red laser (wavelength λ=650 nm) goes through a narrow slit which is only a=2 microns wide. After the light emerges from the slit, it is visible on a screen that is L=5 meters away from the slit.
What is the approximate width on the screen (in cm) of the bright central spot? Here width is defined as the distance between the center and the first minimum.
Anonymous..!!, I know who you are,now your 8.02x account is being permanently blocked for using unfair means.
To determine the approximate width of the bright central spot on the screen, we can use the concept of diffraction.
Diffraction occurs when light waves pass through a narrow slit and spread out, creating a pattern of bright and dark spots known as a diffraction pattern.
The formula to calculate the angle of the first minimum (θ) in a single-slit diffraction pattern is given by:
sin(θ) = λ / a,
where λ is the wavelength of the light and a is the width of the slit.
In this case, the wavelength of the red laser light is λ = 650 nm = 650 × 10^-9 m, and the width of the narrow slit is a = 2 μm = 2 × 10^-6 m.
Using these values, we can calculate the angle of the first minimum:
sin(θ) = (650 × 10^-9 m) / (2 × 10^-6 m).
Now, we can use the small angle approximation (for small angles, sin(θ) ≈ θ in radians) to simplify the calculation:
θ ≈ (650 × 10^-9 m) / (2 × 10^-6 m).
Finally, we can use trigonometry to find the width on the screen (w) of the bright central spot. The width can be approximated by:
w ≈ 2 × L × tan(θ),
where L is the distance between the slit and the screen.
In this case, L = 5 m.
Now, we can substitute the angle we calculated earlier into the formula:
w ≈ 2 × (5 m) × tan(θ).
By solving this equation, you can find the approximate width of the bright central spot on the screen in centimeters.