1. (a) Consider a thin biconvex lens (as shown in Fig. 3.18) made of
a material whose refractive index is 1.5. The radii of curvature of the
first and second surfaces (R1 and R2) are +100 and –60 cm respectively.
The lens is placed in air (i.e. n1 = n3 = 1). For an object at a
distance of 100 cm from the lens, determine the position and linear
magnification of the (paraxial) image. Also calculate x1 and x2 and
verify Newton’s formula [Eq. (20)].(b) Repeat the calculations of the
above problem when the object is at a distance of 50 cm.... Get solution
2. Consider a thin lens (made of a material of refractive index n2) having different media on the two sides; let n1 and n3 be the refractive indices of the media on the left and on the right of the lens respectively. Using Eq. (5) and considering successive refractions at the two surfaces, derive Eq. (14). Get solution
3. Referring again to Fig. 4.18 assume a biconvex lens with |R1| =100 cm, |R2| = 60 cm with n1 =1.0 but n3 =1.6. For u = –50 cm determine the position of the (paraxial) image. Also determine the first and second principal foci and verify Newton’s formula. Draw the ray diagram. Get solution
4. (a) In Fig 4.18, assume the convex lens to be replaced by a (thin) biconcave lens with |R1| =100 cm, |R2| = 60 cm. Assume n1 = n3 = 1 and n2 = 1.5. Determine the position of the image and draw an approximate ray diagram for u = – 100 cm.(b) In (a), assume n1 = n3 = 1.5 and n2 = 1.3. Repeat the calculations and draw the ray diagram. What is the qualitative difference between the systems in (a) and (b). Get solution
5. Consider an object of height 1 cm placed at a distance of 24 cm from a convex lens of focal length 15 cm (see Fig. 4.19). A concave lens of focal length – 20 cm is placed beyond the convex lens at a distance of 25 cm. Draw the ray diagram and determine the position and size of the final image....Fig. 4.19 An optical system consisting of a thin convex and a thin concave lens. All distances are measured in centimeters. Get solution
6. Consider a thick biconvex lens whose magnitude of the radii of curvature of the first and second surfaces are 45 and 30 cm respectively. The thickness of the lens is 5 cm and the refractive index of the material, it is made of, is 1.5. for an object of height 1 cm at a distance of 90 cm from the first surface, determine the position and size of the image. Draw the ray diagram for the axial point of the object. Get solution
7. In the above problem assume that the second surface is silvered so that it acts like a concave mirror. For an object of height 1 cm at a distance of 90 cm from the first surface determine the position and size of the image and draw the ray diagram. Get solution
8. Consider a sphere of radius 20 cm of refractive index 1.6 (see Fig. 4.20). Show that the paraxial focal point is at a distance of 6.7 cm from the point P2.... Get solution
9. Consider a hemisphere of radius 20 cm and refractive index 1.5. Show that parallel rays will focus at a point 40 cm from P2 (see Fig. 4.21).... Get solution
10. Consider a lens of thickness 1 cm made of a material of refractive index 1.5, placed in air. The radii of curvature of the first and second surfaces are +4 cm and –4 cm respectively. Determine the point at which parallel rays will focus. Get solution
2. Consider a thin lens (made of a material of refractive index n2) having different media on the two sides; let n1 and n3 be the refractive indices of the media on the left and on the right of the lens respectively. Using Eq. (5) and considering successive refractions at the two surfaces, derive Eq. (14). Get solution
3. Referring again to Fig. 4.18 assume a biconvex lens with |R1| =100 cm, |R2| = 60 cm with n1 =1.0 but n3 =1.6. For u = –50 cm determine the position of the (paraxial) image. Also determine the first and second principal foci and verify Newton’s formula. Draw the ray diagram. Get solution
4. (a) In Fig 4.18, assume the convex lens to be replaced by a (thin) biconcave lens with |R1| =100 cm, |R2| = 60 cm. Assume n1 = n3 = 1 and n2 = 1.5. Determine the position of the image and draw an approximate ray diagram for u = – 100 cm.(b) In (a), assume n1 = n3 = 1.5 and n2 = 1.3. Repeat the calculations and draw the ray diagram. What is the qualitative difference between the systems in (a) and (b). Get solution
5. Consider an object of height 1 cm placed at a distance of 24 cm from a convex lens of focal length 15 cm (see Fig. 4.19). A concave lens of focal length – 20 cm is placed beyond the convex lens at a distance of 25 cm. Draw the ray diagram and determine the position and size of the final image....Fig. 4.19 An optical system consisting of a thin convex and a thin concave lens. All distances are measured in centimeters. Get solution
6. Consider a thick biconvex lens whose magnitude of the radii of curvature of the first and second surfaces are 45 and 30 cm respectively. The thickness of the lens is 5 cm and the refractive index of the material, it is made of, is 1.5. for an object of height 1 cm at a distance of 90 cm from the first surface, determine the position and size of the image. Draw the ray diagram for the axial point of the object. Get solution
7. In the above problem assume that the second surface is silvered so that it acts like a concave mirror. For an object of height 1 cm at a distance of 90 cm from the first surface determine the position and size of the image and draw the ray diagram. Get solution
8. Consider a sphere of radius 20 cm of refractive index 1.6 (see Fig. 4.20). Show that the paraxial focal point is at a distance of 6.7 cm from the point P2.... Get solution
9. Consider a hemisphere of radius 20 cm and refractive index 1.5. Show that parallel rays will focus at a point 40 cm from P2 (see Fig. 4.21).... Get solution
10. Consider a lens of thickness 1 cm made of a material of refractive index 1.5, placed in air. The radii of curvature of the first and second surfaces are +4 cm and –4 cm respectively. Determine the point at which parallel rays will focus. Get solution
