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A plano-convex lens with the radius of curvature R=-100mm is used to focus white light on a flat screen in air. The refractive index of glass in red light is n=1.5147 and in blue light is n=1.5228. Find the axial color and lateral color in the lens assuming the field angle of w = 5 deg. What should be the distance from the lens to the screen to minimize the chromatic aberration in the image? LATERAL CHROMATIC ABERRATION YELLOW BUE | Δη w Bfde Az AXIAL CHROMATIC ADERRATION Bfdred

Using the Formula torte opucal power ora Tens wering that 1 1 1 1 (n-1) (n-1) (n-1) -100 100 6 - 9 - 00 The front surface has r=-0, so we do not need to account for the lens' thickness The focal length in red and blue light is 100 Fred = 194.3 mm 1.5147 - 1 100 Sour = 191.3 mm 1.5228 - 1 Since the back principal surface coincides with the lens back surface, for this case back focal distance (Bfd) and focal length are the same Bfdred = fred and Bfdblue = folue Axial chromatic aberration (axial colour) is Az = Bfdred - Bfdblue = fred - blue= 3 mm. For the field angle w = 5 deg, the image height is n = f tanw The lateral chromatic aberration (lateral colour) is An = red - blue = Ured - fblue) tanw =(194.3–191.3)0.0875=0.263 mm The best distance for minimum chromatic aberration is d = 191.3+Az/2=192.8 mm, which corresponds to the mid noint between blue and red focal points

A glass sphere with the radius R=500 mm is used as a solar energy concentrator. One can also use it to demonstrate the effect of chromatic aberration in sun light on a white screen. The refractive index of glass in red and blue light is n=1.6676 and n=1.6888, respectively. 1. Prove that for a spherical lens the principal planes coincide, and they are situated exactly at the center of curvature of the sphere. 2. How far from the sphere one should place a screen to form the image of the Sun in red light and in blue light? What is the optimal position to use? use Î111 COLLECTOR BALL LENS TRACING SYSTEM