Monochromatic light (wavelength ) is incident perpendicularly on a single slit (width ). A screen is placed parallel to the slit plane, and on it the distance between the two minima on either side of the central maximum is .
(a) What is the distance from the slit to the screen? (Hint: The angle to either minimum is small enough that .)
(b) What is the distance on the screen between the first minimum and the third minimum on the same side of the central maximum?
(a) The distance of the screen from the slit is .
(b) The distance between the first and third minima is .
Distance between the two minima on either side of the central maxima localid="1663048702619"
Wavelength of incident light
An optical element with a periodic structure that divides light into a number of beams that move in diverse directions is known as a diffraction grating.
The angular distance of the order minima in diffraction pattern produced from a single slit having slit width is
Here, is the wavelength of the incident light.
Let the distance from the slit to the screen be . For small angular distances
Here is the distance measured on the screen. Thus, from equation (i) the separation between the first two minima on either sides of the central maxima is
Substitute the values to get
Thus, the distance is .
From equation (i), the distance between the first and third minima is
Thus, the distance is .
Babinet’s principle. A monochromatic bean of parallel light is incident on a “collimating” hole of diameter . Point P lies in the geometrical shadow region on a distant screen (Fig. 36-39a). Two diffracting objects, shown in Fig.36-39b, are placed in turn over the collimating hole. Object A is an opaque circle with a hole in it, and B is the “photographic negative” of A . Using superposition concepts, show that the intensity at P is identical for the two diffracting objects A and B .
The distance between the first and fifth minima of a single slit diffraction pattern is with the screen away from the slit, when light of wavelength role="math" localid="1663070418419" is used. (a) Find the slit width. (b) Calculate the angle role="math" localid="1663070538179" of the first diffraction minimum.
A beam of light consisting of wavelengths fromis directed perpendicularly onto a diffraction grating with 160 lines/mm. (a) What is the lowest order that is overlapped by another order? (b) What is the highest order for which the complete wavelength range of the beam is present? In that highest order, at what angle does the light at wavelength (c) and (d) appear? (e) What is the greatest angle at which the light at wavelength appears?
Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2000 km. One limitation on such a device is the spreading of the beam due to diffraction, with resulting dilution of beam intensity. Consider such a laser operating at a wavelength of 1.40 nm. The element that emits light is the end of a wire with diameter 0.200 mm. (a) Calculate the diameter of the central beam at a target 2000 km away from the beam source. (b) What is the ratio of the beam intensity at the target to that at the end of the wire? (The laser is fired from space, so neglect any atmospheric absorption.)
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