Light of wavelength 5.4 10 –7 m is incident normally on a diffraction grating.The separation between adjacent lines in the grating is 2.0 10 –6 m. The light that emerges fromthe grating falls on a semicircular screen, as shown in the view from above.diffraction gratingscreenVIEW FROM ABOVElight,wavelength 5.4 10 –7 mThe grating is at the centre of the semicircle, and the lines of the grating are vertical.How many bright dots are formed on the screen?A 3 B 4 C 6 D 7
Question
Light of wavelength 5.4 10 –7 m is incident normally on a diffraction grating.The separation between adjacent lines in the grating is 2.0 10 –6 m. The light that emerges fromthe grating falls on a semicircular screen, as shown in the view from above.diffraction gratingscreenVIEW FROM ABOVElight,wavelength 5.4 10 –7 mThe grating is at the centre of the semicircle, and the lines of the grating are vertical.How many bright dots are formed on the screen?A 3 B 4 C 6 D 7
Solution
To solve this problem, we need to use the formula for the diffraction grating, which is:
dsin(θ) = mλ
where: d = separation between adjacent lines in the grating = 2.0 x 10^-6 m λ = wavelength of the light = 5.4 x 10^-7 m m = order of the diffraction pattern θ = angle of diffraction
We are looking for the number of bright dots, which corresponds to the number of orders (m) that fit within the semicircular screen.
First, we need to find the maximum order (m) that fits within the screen. To do this, we set θ = 90 degrees (since the light can't diffract more than 90 degrees from the normal), and solve for m:
dsin(90) = mλ 2.0 x 10^-6 = m*5.4 x 10^-7 m = 2.0/5.4 = 3.7
Since m must be an integer, the maximum order that fits within the screen is m = 3.
However, for each order, there are two bright dots (one on each side of the central dot). So the total number of bright dots is 2*m + 1 (the +1 accounts for the central dot).
So the total number of bright dots is 2*3 + 1 = 7.
Therefore, the correct answer is D) 7.
Similar Questions
30 The equation = ndsinis used to calculate the wavelength of light in an experiment that uses a diffraction grating. Thelight from the diffraction grating is displayed on a screen.What do the symbols n and d represent?n dA number of slits in the grating distance between adjacent slits in the gratingB number of slits in the grating distance from grating to screenC order of intensity maximum distance between adjacent slits in the gratingD order of intensity maximum distance from grating to screen31 The diagram shows a metal block.abcI IThe block has sides of length a, b and c as shown, and its volume is V. Each charge carrier has acharge –q and the number density of the charge carriers in the metal is n. It takes each chargecarrier an average time of t to pass through the block.What is an expression for the current I ?A I = nqabc B I = nqVt C I = nqbct D I = nqaV
From the diffraction grating to the screen is 1 m. When the grating is illuminated by monochromatic light with a wavelength of 500 nm, the distance between the central and first maxima on the screen is 1 cm.How many strokes per millimeter are there in this grating?
A diffraction grating, which has 4000 lines/cm is used at normal incidence. Calculatethe dispersive power of the grating in the third order spectrum in the wavelengthregion 5000Å.
The diffraction grating contains 100 strokes per 1 mm. The distance from the grid to the screen is 5 m. The grid is illuminated with white light (wavelengths from 400 nm to 780 nm). What is the width of the spectrum of the first order?
5. A single slit of width 0.05 mm is illuminated with monochromatic light of wavelength 500nm. Calculate the intensity of light at an angle of 20∘ relative to the central maximum on a distant screen.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.