1. Consider a system of two thin convex lenses of focal lengths 10
cm and 30 cm separated by a distance of 20 cm in air.(a) Determine the
system matrix elements and the positions of the unit planes(b) Assume a
parallel beam of light incident from the left. Use Eq. (67) and the
positions of the unit planes to determine the image point. Using the
unit planes draw the ray diagram.[Ans. (a) a =1/15, b =1/3, c = -1, d =
-20; the first convex lens is in the middle of the two unit planes. (b)
The final image is virtual and is 15 cm away (on the left) from the
second lens.] Get solution
2. Consider a thick biconvex lens whose magnitudes of the radii of curvature of the first and second surfaces are 45 cm and 30 cm respectively. The thickness of the lens is 5 cm and the refractive index of the material of the lens is 1.5. Determine the elements of system matrix and positions of the unit planes and use Eq. (67) to determine the image point of an object at a distance of 90 cm from the first surface.[ Ans. a = 0.02716, b = 0.9444, c = 0.9630, d = –3.3333, du1 =2.0455, du2 = –1.3636. Final image at a distance of 60 cm from the second surface.] Get solution
3. Consider a hemisphere of radius 20 cm and refractive index 1.5. If H1 and H2 denote the positions of the first and second principal points, then show that AH1 = 13.3 cm and that H2 lies on the second surface as shown in Fig. 4.13. Further, show that the focal length is 40 cm.... Get solution
4. Consider a thick lens of the form shown in Fig. 4.14; the radii of curvature of the first and second surfaces are – 10 cm and +20 cm respectively and the thickness of the lens is 1.0 cm. The refractive index of the material of the lens is 1.5. Determine the positions of the principal planes.[ Ans. du1= 20/91 cm, du2 = – 40/91 cm]... Get solution
5. Consider a combinations of two thin lenses of focal lengths f1 and f2 separated by a distance (f1 + f2). Show that the angular magnification of the lens combinations (which is just ...) is given by – f1/f2. Interpret the negative sign in the expression for magnification. Get solution
6. Consider a spherical refracting surface as shown in Fig. 3.12. Using matrix method show that for an object at a distance of ...from the surface, the image is virtual and at a distance of ...from the surface. Get solution
2. Consider a thick biconvex lens whose magnitudes of the radii of curvature of the first and second surfaces are 45 cm and 30 cm respectively. The thickness of the lens is 5 cm and the refractive index of the material of the lens is 1.5. Determine the elements of system matrix and positions of the unit planes and use Eq. (67) to determine the image point of an object at a distance of 90 cm from the first surface.[ Ans. a = 0.02716, b = 0.9444, c = 0.9630, d = –3.3333, du1 =2.0455, du2 = –1.3636. Final image at a distance of 60 cm from the second surface.] Get solution
3. Consider a hemisphere of radius 20 cm and refractive index 1.5. If H1 and H2 denote the positions of the first and second principal points, then show that AH1 = 13.3 cm and that H2 lies on the second surface as shown in Fig. 4.13. Further, show that the focal length is 40 cm.... Get solution
4. Consider a thick lens of the form shown in Fig. 4.14; the radii of curvature of the first and second surfaces are – 10 cm and +20 cm respectively and the thickness of the lens is 1.0 cm. The refractive index of the material of the lens is 1.5. Determine the positions of the principal planes.[ Ans. du1= 20/91 cm, du2 = – 40/91 cm]... Get solution
5. Consider a combinations of two thin lenses of focal lengths f1 and f2 separated by a distance (f1 + f2). Show that the angular magnification of the lens combinations (which is just ...) is given by – f1/f2. Interpret the negative sign in the expression for magnification. Get solution
6. Consider a spherical refracting surface as shown in Fig. 3.12. Using matrix method show that for an object at a distance of ...from the surface, the image is virtual and at a distance of ...from the surface. Get solution
