Constants Part A The left end of a long glass rod 8.40 cm in diameter, with an i

Question

Constants Part A The left end of a long glass rod 8.40 cm in diameter, with an index of refraction 1.65, is ground and polished to a convex hemispherical surface with a radius of 4.20 cm. An object in the form of an arrow 1.47 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 Find the position of the image of the arrow formed by paraxial rays incident on the convex surface cm Submit Request Answer Part B Find the height of the image of the arrow formed by paraxial rays incident on the convex surface Submit Request Answer Part C Is the image erect or inverted? O erect O inverted Submit Request Answer

Explanation / Answer

Given that,

n2 = 1.65

n1 = 1

radius, R = -4.2 cm

object height, y = 1.47 mm

object distance, s = -24.5 cm

(a)

From the refraction formula,

n2 / s' - n1 / s = n2 - n1 / R

(1.65 / s') - (1 / -24.5) = (1.65 - 1) / -4.2

1.65 / s' = -0.1955

lmage position, s' = -8.43 cm

(b)

Magnification, M = -s' / s = y' / y

8.43 / 24.5 = y' / 1.47

y' = 0.506 mm

(c)

As the image distance is negative so the image is inverted.

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