A periscope. 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 p1 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? (Use any variable or symbol stated above as necessary.)
d = behind the lower mirror

(b) What is its magnification?

a) d = p1+h

b) magnification = 1

Explanation:

Periscopes are made with flat mirrors. A flat mirror  a number of properties, including:

the image produced is upright

the image is the same size as the object (i.e., the magnification is m = 1)

the image is the same distance from the mirror as the object appears to be (i.e., the image distance = the object distance)

the image is a virtual image, as opposed to a real image, because the light rays do not actually pass through the image. This also implies that an image could not be focused on a screen placed at the location where the image is.

a) The upper Mirror M₁ produces a virtual actual sized image l₁ with q₁= -p₁ and M₁ = -q₁/p₁ =1.

The object for mirror M₂, at object distance  p₂ = p₁ + h

The lower Mirror M₁ produces a virtual actual sized image, right side up, l₁ with q₂= -p₂ = p₁ + h and M₂ = -q₂/p₂ =1 and also M₁M₂ = 1.

Therefore the distance of the final image from the lower mirror  is

d = p₁ + h behind the lower mirror.

b) Since periscopes are made with flat mirrors and one of characteristics  is that the image is the same size as the object, which means that the magnification is 1.

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