A plano-concave lens having index of refraction 1.50 is placed on a flat glass plate as shown in the figure below. Its curved surface, with radius of curvature 8.35 m, is on the bottom. The lens is illuminated from above with yellow sodium light of wavelength 592 nm, and a series of concentric bright and dark rings is observed by reflection. The interference pattern has a dark spot at the center that is surrounded by 42 dark rings, the largest of which is at the outer edge of the lens. (a) What is the thickness of the air layer at the center of the interference pattern? um (b) Calculate the radius of the outermost dark ring. 49.178 cm (c) Find the focal length of the lens. 24.59 m

While on a trip, you see a light on a far away mountain. Your partner tells you that they are actually two lights, close to each other. You take out your telescope to verify this claim. Your telescope has an objective lens of 3 cm diameter. The lights are 10.8 km away from you. Basing only on the diffraction limit, how far apart can they be from each other, so that your telescope will be able to resolve them as two separate lights? Use wavelength of light as 670 nm. Write your answer in meters.

While flying at an altitude of 9.50 km, you look out the window at various objects on the ground. If your ability to distinguish two objects is limited only by diffraction, find the smallest separation between two objects on the ground that are distin- guishable. Assume your pupil has a diameter of 4.0 mm and take A = 575 nm.

A child is playing with a bubble wand, which is a large rectangular wire frame that contains a soap film. The child holds the wand vertically, which causes the film to be thinner at the top and thicker at the bottom, forming a wedge shape. Assume a thickness of essentially zero at the top. White light shines on the film with approximately normal incidence. The child views the reflected light from the film and sees the first violet interference band at a distance of 3.00 cm from the top edge of the film. The index of refraction of the soap film is the same as that of water, n = 1.33, and the wavelength of violet light is 1 = 403 nm. (a) At what distance (in cm) from the top edge of the film does the child see the first red (A = 666 nm) interference band? cm (b) What is the thickness (in nm) of the soap film at the location of the first violet interference band? nm What is the thickness (in nm) of the soap film at the location of the first red interference band? nm (c) What is the wedge…