Question

The left end of a long glass rod 8.00 cm in diameter and with an index of refraction of 1.60 is ground and polished to a convex hemispherical surface with a radius of 4.00 cm . An object in the form of an arrow 1.90 mm tall, at right angles to the axis of the rod, is located on the axis 24.5 cm to the left of the vertex of the convex surface.

1)Find the position of the image of the arrow formed by paraxial rays incident on the convex surface. Express your answer in centimeters.

2)Find the height of the image formed by paraxial rays incident on the convex surface. Express your answer in millimeters.

3)Is the image upright or inverted?

Answer 1

. Given, nu = 1 (air). = 2106 for glass S = 24.5cm = 0.245m R = 0.4m pasta object - image relationship. for Spherical reflecting surface + 12 21 5 enn, s' & s'= n2 1 ng S R 1.6 -11 0:04 0.245 -) S'E 0.146542 m S = 14.65 cm Pout(b) The position of image as 14065 cm to the right of the verks, lateral magnification for spresical refracting surface. m = ns' 95 y > y = -ms'y S Sy'= - 0) (0.14684) (1.9x103) (1•6) (0.245) 0.000710 2R > 45 0.71 mm HY LE 071mm Hence, height of image is 0.71 man. magnification, m=yl = -0.37 .mto y Giolle, magnification is negative, the image is inveetah part (c), -0. 1.4 tas! (Inverted

. Given, nu = 1 (air). = 2106 for glass S = 24.5cm = 0.245m R = 0.4m pasta object - image relationship. for Spherical reflecting surface + 12 21 5 enn, s' & s'= n2 1 ng S R 1.6 -11 0:04 0.245 -) S'E 0.146542 m S = 14.65 cm Pout(b) The position of image as 14065 cm to the right of the verks, lateral magnification for spresical refracting surface. m = ns' 95 y > y = -ms'y S Sy'= - 0) (0.14684) (1.9x103) (1•6) (0.245) 0.000710 2R > 45 0.71 mm HY LE 071mm Hence, height of image is 0.71 man. magnification, m=yl = -0.37 .mto y Giolle, magnification is negative, the image is inveetah part (c), -0. 1.4 tas! (Inverted