Light-reflection And Refraction

For concave mirror,

The virtual image formed by concave mirror is magnified, that produced by plane mirror is of the same size and that by a convex mirror is diminished.

A convex mirror is used to see the traffic at the back. It is because a convex mirror always forms an erect though diminished image of the object. It has a wider field of view. So, we will be able to much larger at the back than a plane mirror while driving the car.

For an erect image, magnification is positive. Thus, m = 3 for an erect image three times the size of the object.
m = 3

For a concave mirror,

⇒v = -3u
Using Mirror formula,

Putting the value of v = -3u


v = -3u
⇒ v = 36 cm
Thus, the image is formed behind the mirror at a distance of 36 cm.

As the object is moved from infinity towards the pole of a concave mirror, the image formed starts shifting from the focus of the mirror towards infinity.
When the object is at infinity, the image is formed at the focus or in the focal plane.
As the object is shifted, the image is formed between the focus and the centre of curvature, then at the centre of curvature, then beyond the centre of curvature, then at infinity and finally the image is formed behind the mirror.

(i)

(ii)

(iii)
The image is virtual, erect and larger than the object.

Given, height of object = + 3 cm
object distance(v) = 9 cm
focal length of concave mirror(f) = 18 cm
Using Mirror formula,
For concave mirror, f = -18 cm, u = 9 cm



Using Magnification equation,



Thus, the image will be real, inverted and larger than the object.

(i) When object is beyond the centre of curvature

(ii) When the object is at the centre of curvature

For a thick plane mirror, first reflection will take place through the glass surface and the second through the silvered surface. The silvered surface is much more reflective than the glass surface. The third reflection will be after reflection from front and then from the silvered surface. So, the second reflection will be more effective and the second image will be the brightest.

The arrow pointing north-east will have be resultant of two directions- north and east. The horizontal component of arrow facing east will be same on reflection. But the vertical component of arrow facing the plane mirror will be reflected and be reversed. Thus, the image will have an arrow resultant of south and east direction.

The size of the image does not change when the mirror is rotated by a certain angle. But the reflected ray rotates twice the angle of rotation of incident ray.

Given,
focal length of mirror(f) = 12 cm
⇒u = -3v
Using Mirror formula,



As v is positive, so image is formed at 8 cm behind the mirror.

A real image is formed when the rays of light are convergent and a virtual image is formed when the rays of light diverge. The convergent rays meet to form a real image and the divergent rays appear to meet to form a virtual image.

The number of images formed if two plane mirrors are kept at an angle θ is given by,
and it is given by
For θ = 72°, number of images is as is an odd number.

A plane mirror produce an image of the same size as the object. Thus, the value of magnification is 1 for a plane mirror.
The formed image is virtual. The magnification is positive for a virtual image. Thus, the magnification by a plane mirror is + 1.

The final image will have the edges perpendicular to principal axes larger than that of the dice. Thus, the shape of dice will be same but with different dimensions like a rectangular parallelepiped.

The number of images formed if two plane mirrors are kept at an angle θ is given by,
and it is given by
For θ = 90°, number of images is as is an even number.
So, 3 images will be formed for each perpendicular mirror pair. Thus, 6 images will be formed, 3 for adjacent walls and 3 for wall and ceiling mirrors.

A convex spherical mirror always produces a virtual, erect and diminished image of an object.

A convex mirror always produces a diminished virtual and erect image for a real object.

The image is formed between the pole and the focus of a convex mirror for an object placed between infinity and the pole of the mirror.

A light ray incident normally on a plane surface traces back its path. The angle of deviation is the angle between produced incident ray and reflected ray.
The angle of deviation is 180° for the above case.

A convex mirror always forms a virtual, erect and diminished image for a real object irrespective of its position.

The radius of curvature of the mirror is double the focal length (R = 2f). The image formed at the centre of curvature of the concave mirror is real, inverted and of the same size.
For the given mirror, the center The object distance is equal to the centre of curvature of the concave mirror.

Total number of images formed by two mirrors at right angles is . But only one image will have the man with comb in his right hand. This image is produced by the imaginary mirror created between dual reflection. Thus, two images will have the man combing with left hand.

False
The Laws of reflection are valid for any reflecting surface including spherical surfaces. So, they are valid for both plane and curved mirrors.

False
The radius of curvature of a spherical mirror is twice of its focal length. (R = 2f)

True

False
A convex always produces a diminished image of the object. It can never produce an image larger than the size of the object.

True

True
When a small lamp is kept at the focus of the concave mirror, the rays of light emitted from the lamp after reflection on its surface passes parallel to the principal axis.

False
A plane mirror always produces a virtual image for a real object.

True
When an object is kept between the focus and pole of a concave mirror, a virtual, magnified and erect image is obtained behind the mirror.

False
When a plane mirror is turned by a angle θ, the reflected rays turns by an angle 2θ.

True
In a plane mirror, the image distance is equal to the object distance.

False
The number of images formed if two plane mirrors are kept at an angle θ is given by,
and it is given by
For θ = 45°, number of images is as is an even number.

True

False
Mirror formula is a relation between the object distance, image distance and the focal length of a mirror.
Magnification formula deals with the height of the image and the height of the object.

True
Mirror formula does not change for concave and convex mirror. The sign conventions are changed according to the nature of mirror.

True
Magnification formula deals with the height of the image and the height of the object.

True
The Magnification equation is not changed for convex and concave mirror. The height of the object and the height of the image are taken positive or negative as per the nature of mirror.