A lens has focal length f=40 cm. Find the type and height of the image produced when a 2.6-cm-h

step 1 Given that focal length equals 35 centimeter for part A, object distance S equals f plus 10 equa

A lens has focal length f=40 cm. Find the type and height...

A lens has focal length $f=40 \mathrm{~cm}$. Find the type and height of the image produced when a $2.6$-cm-high object is placed at distances (a) $f+10 \mathrm{~cm}$ and (b) $f-10 \mathrm{~cm}$.

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Key Concepts

Thin Lens Equation

This fundamental equation, given by 1/f = 1/d_object + 1/d_image, relates the focal length of a lens with the distances of the object and its image from the lens. It is essential for determining where the image forms and whether it is real or virtual, particularly by comparing the object distance to the focal length.

Magnification and Image Height

Magnification is defined as the ratio of the image height to the object height and can be calculated using m = -d_image/d_object. The sign of the magnification indicates whether the image is inverted (negative) or upright (positive), and its magnitude shows how the image size compares to the object size.

Real and Virtual Images

Images formed by a lens can be categorized as real or virtual. When the object distance is greater than the focal length, a converging lens produces a real image that is inverted and can be projected on a screen. Conversely, when the object is within the focal length, the lens produces a virtual image that is upright and cannot be projected, with the apparent image formed on the same side of the lens as the object.

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