A periscope (Figure P 36.6 ) is useful for viewing objects...

A periscope (Figure $\mathrm{P} 36.6 )$ is useful for viewing objects that cannot be seen directly. It finds use in submarines and in watching golf matches or parades from behind a crowd of people. Suppose that the object is a distance $p_{1}$ from the upper mirror and that the two flat mirrors are separated by a distance $h .$ (a) What is the distance of the final image from the lower mirror? (b) Is the final image real or virtual? (c) Is it upright or inverted? (d) What is its magnification? (e) Does it appear to be left-right reversed?

Key Concepts

Magnification in Mirror Systems

Magnification is defined as the ratio of the image size to the object size. In plane mirrors, the magnification is usually one, meaning the image size is the same as the object size, though additional considerations such as the arrangement of mirrors might affect the overall perception of size.

Lateral (Left-Right) Reversal

In mirror systems, the image often appears to have a reversal of the left-right orientation relative to the object. This lateral inversion is a common feature of reflections in flat mirrors and is important in understanding the final appearance of images in devices like periscopes.

Image Orientation and Inversion

The orientation of an image—whether it appears upright or inverted—is determined by the number and arrangement of reflections. For example, an even number of reflections usually restores the original orientation, while an odd number may invert the image.

Image Distance and Virtual Images

Image distance pertains to the measure from the mirror to the image formed by reflection. In plane mirror systems, the images are typically virtual, meaning they cannot be projected onto a screen because the light rays only appear to diverge from their apparent source.

Multiple Reflections

When light reflects off more than one surface, as in a periscope, each reflection must be considered sequentially. The combined effect of multiple reflections determines properties such as image position, orientation, and whether the final image is real or virtual.

Plane Mirror Image Formation

In plane mirrors, the image of an object is formed behind the mirror at a distance equal to the object’s distance in front of the mirror. This concept underlies the basic behavior of images produced in periscopic devices and similar mirror systems.

Law of Reflection

This principle states that the angle at which light strikes a reflective surface (the angle of incidence) is equal to the angle at which it leaves (the angle of reflection). It is fundamental in understanding how images are formed in mirrors and is applicable regardless of whether there is a single or multiple reflections.

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