Determine the image distance for an object placed 38.3 cm from a convex lens having a focal length of 13.4 cm.

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Consider a thin lens with focal length f = 13.4 cm and an object placed at distance u = 38.3 cm from the lens on the object side.

For a thin lens, the standard relation using magnitudes is v = fu / (u - f).

Plugging in the values: v = (13.4 cm)(38.3 cm) / (38.3 cm − 13.4 cm).

Compute the numerator: 13.4 × 38.3 = 513.22.

Compute the denominator: 38.3 − 13.4 = 24.9.

Divide: v = 513.22 / 24.9 ≈ 20.6 cm.

This positive value indicates the image forms on the opposite side of the lens from the object, i.e., a real image for a convex lens when the object distance is greater than zero and the object is outside the focal length.

A couple of quick checks can help confirm the result:
- Since u (38.3 cm) is greater than f (13.4 cm), the lens should produce a real image on the far side, not a virtual image.
- The image distance being roughly 20.6 cm is less than u, which is typical for a convex lens with the object located beyond the focal point.

If one were to round differently during intermediate steps, the final value might appear as 20.60 cm or 20.64 cm depending on precision, but they are all in the same ballpark for these inputs.

Physics 1 Hon - Bowles - p06/p07 P10.22 - Lesson 6 Exit Ticket

Determine the image distance for an object placed 38.3 cm from a convex lens having a focal length of 13.4 cm.

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