A ray of light is incident on a pane mirror at a certain point. The mirror is capable of rotation about an axis passing through the same point. Prove that if the mirror turns through a certain angle then the reflected ray turns through double the angle.
[no copy or spam or improper is answer is allowed!!
any kind of violation will be reported so be careful, if you don't know then don't reply just quite]
Answers
Answer:
A diagram of an object in two plane mirrors that formed an angle bigger than 90 degrees, causing the object to have three reflections.
A plane mirror is a mirror with a flat (planar) reflective surface.[1][2] For light rays striking a plane mirror, the angle of reflection equals the angle of incidence.[3] The angle of the incidence is the angle between the incident ray and the surface normal (an imaginary line perpendicular to the surface). Therefore, the angle of reflection is the angle between the reflected ray and the normal and a collimated beam of light does not spread out after reflection from a plane mirror, except for diffraction effects.
A plane mirror makes an image of objects in front of it; these images appear to be behind the plane in which the mirror lies. A straight line drawn from part of an object to the corresponding part of its image makes a right angle with, and is bisected by, the surface of the plane mirror. The image formed by a plane mirror is always virtual (meaning that the light rays do not actually come from the image), upright, and of the same shape and size as the object it is reflecting. A virtual image is a copy of an object formed at the location from which the light rays appear to come. However, the image is a laterally-inverted "mirror image" of the object. If a person is reflected in a plane mirror, the image of his right hand appears to be the left hand of the image.
Plane mirrors are the only type of mirror for which a real object always produces an image that is virtual, erect and of the same size as the object. Virtual objects produce real images, however.[citation needed] The focal length of a plane mirror is infinity;[4] its optical power is zero.
A ray diagram for a plane mirror. The incident light rays from the object create an apparent mirror image for the observer.
A plane mirror is made using some highly reflecting and polished surface such as a silver or aluminium surface in a process called silvering.[5] After silvering, a thin layer of red lead oxide is applied at the back of the mirror. The reflecting surface reflects most of the light striking it as long as the surface remains uncontaminated by tarnishing or oxidation. Most modern plane mirrors are designed with a thin piece of plate glass that protects and strengthens the mirror surface and helps prevent tarnishing. Historically, mirrors were simply flat pieces of polished copper, obsidian, brass, or a precious metal. Mirrors made from liquid also exist, as the elements gallium and mercury are both highly reflective in their liquid state.
Answer:
Let, XY be the position of mirror initially. A ray AO reflected at O goes along OB.
∠ AON = ∠ BON
∴ ∠ AOY =∠ BOX = α (∵assume)
Let, the mirror be rotated to a new position XY' through an angle ∅ about an axis passing through X. The incident ray, now, gets reflected from O' along O'B'. O'N' is the new position of normal.
According to the law of reflection,
∠AO'N = ∠ B'O'N'
∴ ∠ AO'Y' = ∠B'O'X' = α
Also, ∠ XO'O = ∠ AO'Y' = α
∴ ∠B'O'O = 2α'
Due to rotation of mirror the reflected ray turns through an angle BCB' = θ.
∠ BCB' = ∠ O'CO = θ
∠ O'OC = 180° - 2α
In Δ OO'C, θ + 180° - 2α + 2α' = 180°
or, θ = 2(α-α')
In Δ XOO' , α = ∅ + α'
∴ ∅ = α - α'
Substituting for ∅ in (i), we get θ = 2∅