Monochromatic light falls on two very narrow slits 0.035 mm apart. Successive fringes on a screen 4.80 m away are 5.8 cm apart near the center of the pattern. What is the wavelength of the light?
To find the wavelength of the light, we can use the formula for the fringe separation in a double-slit interference pattern:
\(\Delta y = \frac{{\lambda D}}{{d}}\)
Where:
- \(\Delta y\) is the fringe separation on the screen
- \(\lambda\) is the wavelength of the light
- \(D\) is the distance from the slits to the screen
- \(d\) is the separation between the two slits
Given:
- \(\Delta y = 5.8\) cm = 0.058 m
- \(D = 4.80\) m
- \(d = 0.035\) mm = \(0.035 \times 10^{-3}\) m
Let's plug in these values into the formula and calculate the wavelength of the light:
\(\Delta y = \frac{{\lambda D}}{{d}}\)
\(0.058 = \frac{{\lambda \times 4.80}}{{0.035 \times 10^{-3}}}\)
Now, let's rearrange the equation to solve for \(\lambda\):
\(\lambda = \frac{{0.058 \times 0.035 \times 10^{-3}}}{{4.80}}\)
Calculating this expression:
\(\lambda = \frac{{0.00203 \times 10^{-3}}}{{4.80}}\)
\(\lambda = 4.23 \times 10^{-7}\) m
Therefore, the wavelength of the monochromatic light is \(4.23 \times 10^{-7}\) m or 423 nm.
To find the wavelength of the light, we can use the equation:
wavelength = (distance between the two slits) * (distance to the screen) / (distance between consecutive fringes)
Given values:
Distance between the two slits (d) = 0.035 mm = 0.035 x 10^-3 m
Distance to the screen (D) = 4.80 m
Distance between consecutive fringes (y) = 5.8 cm = 5.8 x 10^-2 m
Plugging in these values into the formula:
wavelength = (0.035 x 10^-3 m) * (4.80 m) / (5.8 x 10^-2 m)
Calculating this expression will give us the wavelength of the light.