A glass rod 96 cm long with an index of refraction of 1.6 has its ends ground to

Question

A glass rod 96 cm long with an index of refraction of 1.6 has its ends ground to convex spherical surfaces of radii 8 cm and 16 cm. A point object is in air on the axis of the rod 19.9cm from the end with the 8 cm radius.

(a) Find the image distance due to refraction at the first surface. (Include the sign.)
_________________ cm

(b) Find the location of the final image distance due to refraction at both surfaces.
______________ cm (from the 8 cm diameter surface)

Ive tried all the chegg solutions and none of them worked for me. Please help me . I've spent numerous hours on this problem.

Explanation / Answer

refraction at a single surface to relate the image and object distances at the surface whose radius is 8.00 cm

n1/s + n2/s' = (n2-n1)/r

s' = n2/[(n2-n1)/r -n1/s]

s = 19.9 cm

n1 = 1 ; n2 = 1.6 r = 8 cm

s' = 64.65 cm

part b )

the object for the second surface = 96 - 64.65 = 31.35 from the surface whose radius is -16 cm

now n1 = 1.6

n2 = 1

s' =  n2/[(n2-n1)/r -n1/s]

s = 31.35 cm

r = -16 cm

s' = -73.87 cm

96 - 73.87 = 22.13 cm from 8cm diameter surface

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