3.Find the angle at which the first diffraction minimum is formed when light of wavelength 632.8nm is sent through: (a) a slit of width 0.1mm; (b) a circular aperture with a diameter of 0.1mn

1)A red low-power laser with λ = 634nm was beamedat a double-slit grating. An interference patternappeared on a screen 2.50 m from the grating. Thedistance from central spot to the next bright spotwas 22.5cm.What is the spacing between the slits in the grating? 2. The red laser (in Q1) is replaced by a blue laserwith a shorter wavelength. All else is the same.Show mathematically whether the interferencepattern it produces will place the bright spots closeror further apart. 3.Given that the blue laser in Q2 has a wavelength of445 nm, calculate the “spot-spacing” for the sameslit grating and screen distance as in Q1. 4.A green laser beam produces spots which are0.334m apart (central to m=1) when a grating is usedwith slits 3,000 nm apart and a screen 1.90m away.What is the wavelength of the laser light?

Given a double slit set up with a spacing of 5.74*10-6m and the light has a wavelength of 618 nm: How far from the central maximum is the third dark fringe (m=2) when the distance between the slits and the screen is 5.00 meters? a) 1.40m b) 2.03m c) 1.30m d) 1.10m (Hint: answer is a)

5. In a location where the speed of sound is 354 m/s, a 2 000-Hz sound wave impinges on two slits 30.0 cm apart. (a) At what angle is the first maximum located? (b) If the sound wave is replaced by 3.00-cm micro- waves, what slit separation gives the same angle for the first maximum? (c) If the slit separation is 1.00 µm, what frequency of light gives the same first maximum angle?

7. The Numerical Aperture, NA, of a waveguide is defined as no sin A where nд is the refractive index of the material from which the light enters the waveguide and is the maximum acceptance angle, as shown in Q3. Apply trigonometry to the figure in Q3 and show that the Numerical Aperture is: √√n²-n² NA =

3. A single slit in an opaque screen is illuminated with a He-Ne laser (A = 1.1522 µm), and on a distant screen it is found that the middle of the tenth dark fringe in the interference pattern lies at an angle 0 = 6.4° from the central maximum. What band of the EM spectrum does this wavelength of light belong to? (a) (b) What is the width of the slit? (b) (c) tween the slit and the distant screen is immersed in water (n = 1.33) rather than At what angle (in degrees) will this minimum appear if the region be- air? (c)

3. In the double-slit experiment, suppose the electric fields of the two waves arriving at a point P on the screen is given by E1 = sin(1015t) in μV/m E2 = sin(1015t + 24 rad) in μV/m where time t is in seconds. (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity IP at point P to the intensity Icen at the center of the interference pattern? (c) Describe where point P is in the interference pattern by giving the order of the maximum or minimum on which it lies, or the order of the maximum and minimum between which it lies.

1. The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.1 mm-diameter pupil, assuming an average wavelength of 570 nm? rads (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 0.8 m apart? r= km (c) What is the distance between two just-resolvable points held at an arm's length (1 m) from your eye? mm S=

White light is incident on a diffraction grating with 455 lines/mm. HINT (a) Calculate the angle 0, (in degrees) to the second-order maximum for a wavelength of 640 nm. r2 16.92 (b) Calculate the wavelength in nm of light with a third-order maximum at the same angle 0 r2' nm