show all work thanks A glass rod 96 cm long with an index of refraction of 1.6 h

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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 20 cm from the end with the 8 cm radius. (a) Find the image distance due to refraction at the first surface. (Include the sign.) 5.5 cm (b) Find the location of the final image distance due to refraction at both surfaces. cm (from the 8 cm diameter surface) (c) Describe the final image. real virtual inside the rod outside the rod

Explanation / Answer

Given that,

length of rod = L = 96 cm

n(glass) = 1.6

R1 = 8 cm

R2 = 16 cm

diatance of object from first lens = u = 20 cm

let image distance at first lens = v

Use the formula,

n(air) / u + n(glass) / v = ng - na / R1

1 / 20 + 1.6 / v = 1.6 - 1 / 8

by solving,

v = 64 cm

(b)

let the final image distance = v2

n(air) / u2 + n(glass) / v2 = ng - na / R2

u2 = 96 - 20 = 76 cm

1 / 76 - 1.6 / v2 = 1.6 - 1 / 16

by solving,

v2 = 32.42 cm

(c)

The final image is real.

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