OPTI 201R Midterm 2 November 10, Problems 1-10 are worth 2.5 points each. Problems are worth 25 points each.

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1 OPTI 20R Midterm 2 November 0, 205 Answer all questions Show your work Partial credit will be given Don t spend too much time on any one problem Use separate sheets o paper and don t cram your work into the spaces below As in the notes, zf and z F are the object and image distances measured rom the ront and rear ocal points The distances z and z are the object and image distances measured rom the ront and rear principal plane Problems -0 are worth 25 points each Problems -3 are worth 25 points each Given the object distance zf = mm, an object space index n = 50, and a lens o eective ocal length E = mm, what is the ront ocal length F and the magniication m? The ront ocal length is given by F = -(50)(80000) = mm The magniication is given by m = (50)(80000) / (60000) = Given the object distance zf = mm, an object space index n = 33, and a magniication m = 500 mm, what is the eective ocal length E and the ront ocal length F? The eective ocal length is given by E = -(500)(-20000) / 33 = mm The ront ocal length is given by F = -33(-35338) = Given the image distance z'f = mm, an object space index n' = 33, and a lens o rear ocal length 'R = mm, what is the eective ocal length E and the magniication m? The eective ocal length is given by E = (-400) / 33 = mm The magniication is given by m = -(80000) / (33(-30075)) = Given the object distance zf = mm, object space index n = 50, image distance z'f = and image index n' = 50, what is the eective ocal length E and the magniication m? The eective ocal length is given by E = Sqrt[-(( )/50) ((40000)/50)] = 555 mm

2 The magniication is given by m = -(40000) / (50(555)) = Given the object distance zf = mm, the ront ocal length F = mm and the rear ocal length 'R = mm, what is the image distance z'f and the magniication? The image distance is given by z'f = (-20000)(80000) / (200000) = mm The magniication is given by m = -(-20000) / (200000) = Given the object distance z = mm, an object space index n = 33, and a lens o ront ocal length F = mm, what is the eective ocal length E and the magniication m? The eective ocal length is given by E = -(20000) / 33 = mm The magniication is given by m = (20000) / ((20000) - (-60000)) = 0 7 Given the image distance z' = mm, an image space index n' = 50, and a lens o rear ocal length 'R = mm, what is the eective ocal length E and the magniication m? The eective ocal length is given by E = (40000) / 50 = mm The magniication is given by m = ((40000) - (40000)) / (40000) = Given the object distance z = mm, an object space index n = 50, and a lens o eective ocal length E = mm, what is the ront ocal length F and the magniication m? The ront ocal length is given by F = -50(-80000) = mm The magniication is given by m = (20000) / ((20000) - (-60000)) = Given the image distance z' = mm, an image space index n' = 33, and a lens o eective ocal length E = mm, what is the rear ocal length 'R and the magniication m?

3 The rear ocal length is given by 'R = 33(40000) = mm The magniication is given by m = ((53200) - (-80000)) / (53200) = Given the object distance z = mm, an object space index n = 00, the image distance z' = mm, an image space index n' = 00, what is the eective ocal length E and the magniication m? The eective ocal length is given by E = 0 / [(00/(40000) - 00/(60000))] = mm The magniication is given by m = ((40000)/00) / ((60000)/00) = 2333 Keep going, more questions on the next page A Cooke triplet consists o three thin lenses in air The eective ocal lengths o the lenses are = 444 mm, 2 = 22 mm and 3 = 444 mm The lenses are separated by t = = 53 mm Do the ollowing: (a) Sketch the lens and label the lens vertices, V, V2, and V3 t2 (b) Using Gaussian reduction, ind the overall ocal length o the lens The thin lens powers are given by = = mm 2 = = mm 2 - -

4 3 = = mm 3 - (c) Where are the principal planes located with respect to the vertices V and V3? Calculate the new distance t 2 between P 2 and P 3 t = t d = = mm Next, reduce the two remaining systems φ d - 23 = φ2 + φ3 - t 2φ2φ3 = 00mm φ 3 23 = t2 φ23 d φ = mm 2 23 = t2 φ23 = mm

5 So, the rear principal plane is mm to let o V 3 From the symmetry o the lens or rom combining all o the results, the ront principal plane is mm to the right o V 2 A Cassegrain telescope has two relective mirrors The irst mirror has a radius o curvature o R = 000 mm The second mirror lies to the let o the irst mirror such that t = 400 mm The radius o curvature o the second mirror is R2 = 250 mm (a) Sketch the telescope and label the vertices, V and V2 (b) Using Gaussian reduction, ind the overall ocal length o the telescope The eective ocal length is φ E = = 2500 mm φ 2

6 (c) Where are the principal planes located with respect to the vertices V and V2? 3 A thick lens has air ( n = ) on the object side and water ( n 2 = 33 ) on the image side The lens is 20 mm thick and has a reractive index o n =5 The radii o curvature o the lens are R = 50 mm and R2 = 40 mm, respective (a) Sketch the lens and label the vertices, V and V2 (b) Using Gaussian reduction, ind the overall ocal length o the lens

7 The eective ocal length is E = = mm 2 (c) Where are the principal planes located with respect to the vertices V and V2? (d) Where are the nodal points located? The rear ocal length is given by = n mm R 2 E = The ront ocal length is given by F = = 7308 mm E The distance to the nodal points is P N = P N = mm 2 2 R F =