A first order spectrum is obtained using an optical grating with 500 lines/m. What is the angular separation of red , with wavelength 700nm and violet, with wavelength 400nm
To find the angular separation between the red and violet light in a first-order spectrum, we can use the formula:
θ = λ / d
where θ is the angular separation, λ is the wavelength of light, and d is the distance between adjacent lines on the grating.
In this case, we are given that the grating has 500 lines/m, which means that the distance between adjacent lines (d) is the reciprocal of this value:
d = 1 / (lines/m)
d = 1 / (500 lines/m)
Now we can calculate the angular separation for both the red and violet light.
For red light with a wavelength of 700nm:
θ_red = 700nm / d
θ_red = 700nm / (1 / (500 lines/m))
θ_red = 700nm * (500 lines/m)
θ_red = 350,000 lines
Similarly, for violet light with a wavelength of 400nm:
θ_violet = 400nm / d
θ_violet = 400nm / (1 / (500 lines/m))
θ_violet = 400nm * (500 lines/m)
θ_violet = 200,000 lines
Therefore, the angular separation between the red and violet light in the first-order spectrum is 350,000 - 200,000 = 150,000 lines.
Please note that the term "lines" here refers to the number of lines on the grating, not the actual distance traveled by the light. It reflects how the grating splits the light into different orders.