Question

An object of length 2 cm is placed in front of a convex lens perpendicular to its axis, having focal length of 20 cm. Distance of the object from the lens is 30 cm. Find the position and nature of the image.

Hint:

For convex lenses, when the object is beyond the focal point, the image formed is real, inverted, and on the opposite side of the object.

Answer 1

Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where: - \( f = 20 \, \text{cm} \) (focal length), - \( u = -30 \, \text{cm} \) (object distance; negative as per sign convention), - \( v \) is the image distance (unknown).
Substitute the known values into the lens formula: \[ \frac{1}{20} = \frac{1}{v} - \frac{1}{-30} \] \[ \frac{1}{v} = \frac{1}{20} + \frac{1}{30} \] To simplify: \[ \frac{1}{v} = \frac{3 + 2}{60} = \frac{5}{60} \] \[ v = 12 \, \text{cm} \] The positive value of \( v \) indicates that the image is formed on the opposite side of the object, which means it is a real and inverted image.