A periscope (Fig. P23.5) is useful for viewing objects that...

A periscope (Fig. P23.5) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance $p_{1}$ from the upper mirror and the centers of 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?

A periscope (Fig. P23.5) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance $p_{1}$ from the upper mirror and the centers of 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

Lateral Inversion

Lateral inversion is the phenomenon where the image is reversed from left to right compared to the object. This occurs in plane mirror reflections, meaning that even though the image is the correct size and orientation vertically, the left and right sides are swapped, a characteristic feature of periscope imaging.

Magnification in Mirror Systems

Magnification is a measure of how the size of an image compares to the size of the object. For plane mirrors, the magnification is 1, as they produce images that are the same size as the objects. This concept is essential in understanding the scale and true representation of images in optical setups.

Law of Reflection

This principle states that the angle of incidence is equal to the angle of reflection. In optical devices like periscopes, this law governs the redirection of light rays off mirrors, ensuring that light from an object is correctly relayed from one mirror to the next to produce an image.

Image Formation in Plane Mirrors

Plane mirrors create images by reflecting light such that the distance behind the mirror (where the image appears) equals the distance of the object in front of it. This process leads to the formation of images that share the size and shape of the object, although the image is virtual and cannot be projected onto a screen.

Real vs Virtual Images

Real images occur when light rays converge and can be captured on a screen, whereas virtual images appear to diverge from a point behind the mirror. In systems using plane mirrors, such as periscopes, the images formed are virtual, indicating that the observer sees an image that seems to exist behind the mirror.

Transcript

00:01 For this problem on the topic of mirrors and lenses, we are shown in the figure a periscope which can be used for objects that cannot be seen directly.

00:09 It is mainly used in submarines.

00:12 Now we are to suppose that an object is a distance p1 from the upper mirror and the centres of the two flat mirrors are separated by a distance h.

00:21 We want to know the distance of the final image from the lower mirror.

00:26 We want to know if this final image is real or virtual, upright or inverted, its magnification, and we want to know if the image will appear left, right, reversed.

00:38 Now when an object is in front of a plane mirror, that mirror forms an upright virtual image that is the same size of the object and as far behind the mirror as the object is in front of the mirror.

00:48 Now this statement is true even if the mirror is rotated, as shown in the ray diagrams that we have here.

00:55 Now in figure a, which is the figure on the left, the real object o1 is a distance p1 in front of the upper mirror in the periscope.

01:06 This mirror forms the virtual image i1 at a distance p1 behind the mirror, as shown in figure b.

01:13 This image serves as the object for the lower mirror in the periscope and is distance p2 is equal to p1 plus h in front of the lower mirror.

01:22 The lower mirror then forms the final image i2, an upright version.

01:26 Image located a distance p2 which is p1 plus h behind the mirror...

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