More problems for Chapter 1 of Introduction to Wave Phenomena (Hirose- Lonngren). In the 18-th century, Bradley observed apparent change in angular location of distant stars by " when the earth is moving normal to the line of sight. Showing first that the earth circulation velocity v about the sun is 3 10⁴ m/s, estimate the light velocity c from the aberration formula v θ =. c (Hint: If you run in rain, the path of rain drops is not normal but tilted.) 3. Rainbow is caused by prism action of spherical water drop. The deviation angle for red light is about 4 and that for violet is about 40. The water index of refraction for red light is 1.33 and for violet light it is 1.35. Find the deviation angles between white incident ray and red and violet refracted rays. Hint: First show that the incident angle θ and deviation angle are related through sinθ = n sin ( θ /) + 4 Determine max by trial and error. θ air (n=1) θ r water (n) 4. Show that the deviation angle β due to double reflections by mirrors intersecting at angle is given by β = π irrespective of the angle of incidence. (Retro-reflectors use = 90, β = 0.) mirror 1 β mirror
5. Light beam falls on a glass slab of index of refraction n and thickness t at incident angle θ. Show that the deviation distance is given by = t ( sinθ cosθ tanθ r ) where θ r is the refraction angle related to θ through the Snell's law sinθ = nsinθ r t θ 6. Find the deviation angle when a light beam is incident at an angle 40 on a prism. The index of refraction of glass is n g = 1.5. At what incident angle does the minimum deviation min occur? What is min? N 40 r r' i' 7. A lens made of glass (n = 1.5) has a focal length of 15 cm in air. If it is placed in water which has an index of refraction n=1.34, what is the focal length? 8. The three lens system simulates a zoom lens. The position of the second lens d is adjustable while the distance between the first and third lens is fixed at cm. For an object distance at 100 cm from the first lens, find the image location and magnification when the second lens is at (a) 10 cm and (b) 30 cm from the first lens. 10 0 10 d 9. A person with hyperopia (farsightedness) wears contact lenses having f = 31.5 cm. (The inverse of the focal length in meters is called Dioptric power. The contact lens has power of +3. D.) If the contact lenses are to be replaced with spectacle lenses worn 17 mm in front of the eyes, what should the focal length of the glasses be? Assume.5 mm for the eye size which would be the normal focal length of the eye lens without effort.
30. (a) Find the effective focal length f eff of a two-lens system with f 1 = 10 cm, f = 15 cm with separation d = 5 cm. (b) Locate the principal planes of the two lenses. (c) The formal lens formula 1 1 1 + = o i f eff holds provided the object distance o is measured from the principal plane H1 and image distance i from H. Find the image location and magnification of an object placed at 30 cm from the first lens. 31. Find the effective focal length and the positions of the principal planes of the thick lens shown. The glass index of refraction is n = 1.5. If an object is placed at 30 cm from the first vertex, where is its image formed? Magnification? (As you will find, H is to the left of H1 in this problem.) 40 cm n = 1.5 R = 15 cm R1 = 10 cm 3. The matrix of a biconcave thick lens is given by 1.1333 1.3333 0.15667 1.0667 The curvature radius of the first surface is 5 cm, the glass index is 1.5 and the lens thickness is cm. Find the other curvature radius. 33. In the mirror-lens system shown, when viewed from right, two images with magnifications ±1.5 are observed at the same location. Determine the object location and the focal length of the mirror. Hint: There are two solutions. 40 cm x f=10 cm
34. A telescope consists of an objective lens with f o = 50 cm and eyepiece with f e =.5 cm. If it is used to view an object 10 m away with image to be formed at 5 cm, what is the separation distance of the lenses? What is the magnification? 35. What is the magnification of the telescope shown for an object at infinity? The lens (erector) in between is to make the total magnification positive (e.g., rifle view finder). If the telescope is used to view an object 50 m away with its image formed at 5 cm, what adjustment has to be made? The numbers above the lenses indicate the focal lengths. 10 cm 3.33 cm.5 cm 10 cm 5 cm 10 cm.5 cm 36. An achromatic doublet has a focal length of +8 cm. The Crown component is an equiconvex lens with a common radius R 1 and Flint component is a divergent lens with curvature radii R1 and R. Determine R. Assume the following data: Crown glass n Blue = 1.51, n Red = 1.51; Flint glass n Blue = 1.63, n Red = 1.6. In the figure, R is positive but it could be negative. R1 Crown glass -R1 R Flint glass 37. A glass sphere of radius R has a concentric cubic void of side R. Find the focal point for a paraxial beam. Also find the effective focal length of the "lens". n=1.5 R R 38. A fish is at the center of a spherical bowl with radius R filled with water (n = 4/3). Find the location and magnification of its image.
39. What is the image of the square ( cm by cm) shown? What is the shape and area of the image? cm cm f =15 cm 0 cm 40. In a four lens system with 5 cm separation as shown, the first and third lenses have f = +0 cm and the second and fourth lenses have f = 0 cm. Find the focal point for a paraxial incident ray. f = 0-0 0-0 5 cm 5 cm 5 cm