All but two gaps within a set of venetian blinds have been blocked off to create a double-slit system. These gaps are separated by a distance of 3.1 cm. Infrared radiation is then passed through the two gaps in the
blinds. The angle between the central and the second-order maxima in the interference pattern is 0.54 degrees.
What is the wavelength of the radiation? Answer in units of ìm.
To find the wavelength of the radiation passing through the double-slit system using the venetian blinds, we can use the formula for the fringe spacing in a double-slit interference pattern:
dλ = y * tan(θ)
Where:
- d is the distance between the two gaps in the blinds
- λ is the wavelength of the radiation
- y is the distance between the central maximum and the second-order maximum on the screen
- θ is the angle between the central and the second-order maxima
In this case, the distance between the two gaps in the blinds is given as 3.1 cm (or 0.031 meters), and the angle θ is given as 0.54 degrees.
First, let's convert the angle from degrees to radians by multiplying it by π/180:
θ = 0.54 * π/180 radians
Now we can rearrange the formula to solve for λ:
λ = (y * tan(θ)) / d
Let's substitute the values we have:
λ = (y * tan(0.54 * π/180)) / 0.031
The only missing value in the equation is the distance y between the central maximum and the second-order maximum on the screen. Since it is not given in the question, we cannot directly calculate the wavelength without this information.