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What is the nature of image formed by convex and concave lens and mirrors and how to show the light reflected by them?

Asked by Vineet J Cheria...(student), on 11/3/11

ntroduction to image formation by lenses:

While attempting to draw the image formation by both convex and concave lenses, we need to know a few rules:

• Any ray of light passing through the optical centre will pass undeviated from its original path.
• Any ray of light moving parallel to the principal axis of the lens will pass through the focus of the lens.
• Any ray of light passing through the focus of a lens will emerge parallel to the principal axis of the lens.

## Image Formation by Convex Lens

Let us first see the image formation by a convex lens:

• When the object is placed at infinity, the image is formed at the focus as shown below by the diagram. The image formed is point sized and is real and inverted.

Object – at infinity

Image – at F

Nature of image – real and inverted

Size of Image – point sized

• When the object is placed between F and 2F, the image is formed beyond 2F. The image is enlarged and is real and inverted.

Object – between F and 2F

Image – beyond 2F

Nature of image – real and inverted

Size of Image – enlarged

• When the object is placed at 2F, the image is also formed at 2F. It is of the same size as that of the object and is again, real and inverted in nature.

Object –at 2F

Image –at 2F

Nature of image – real and inverted

Size of Image – same size as that of object

• When the object is placed beyond 2F, the image is formed between F and 2F. The image at this stage is diminished and is real and inverted.

Object – beyond 2F

Image – between F and 2F

Nature of image – real and inverted

Size of Image – diminished

• When the object is placed between the optic centre, O and F, the image formed is on the same side as that of the object. In this situation, the image is virtual and erect and is enlarged.

Object – between O and F

Image – On the same side as that of the object or behind the lens

Nature of image – virtual and erect

Size of Image – enlarged

• When the object is placed at the focus, F, the image is formed at infinity. The image formed is highly enlarged and is real and inverted.

Object – at F

Image – at infinity

Nature of image – real and inverted

Size of Image – highly enlarged

## Image Formation by Concave Lens

Let us now see the image formation by a concave lens:

• When the object is at infinity, the image is formed at the focus. It is virtual and erect and is point sized.

Object – at infinity

Image – at F

Nature of image – virtual and erect

Size of Image – point sized

• When the object is placed at any point between infinity and the optic centre, the image is always formed between the optic centre, O and F. The image is diminished.

Object – between infinity and the optic centre

Image – between O and F

Nature of image – virtual and erect

Size of Image – diminished

Posted by Prakhar Bindal(student), on 12/3/11

A convex mirror, fish eye mirror or diverging mirror, is a curved mirror in which the reflective surface bulges toward the light source. Convex mirrors reflect light outwards, therefore they are not used to focus light. Such mirrors always form a virtual image, since the focus (F) and the centre of curvature (2F) are both imaginary points "inside" the mirror, which cannot be reached. Therefore images formed by these mirrors cannot be taken on screen. (As they are inside the mirror)

A collimated (parallel) beam of light diverges (spreads out) after reflection from a convex mirror, since the normal to the surface differs with each spot on the mirror.

### Uses

Convex mirror lets motorists see around a corner.

The passenger-side mirror on a car is typically a convex mirror. In some countries, these are labeled with the safety warning "Objects in mirror are closer than they appear", to warn the driver of the convex mirror 's distorting effects on distance perception. Convex mirrors are preferred in vehicles because they give an upright, though diminished, image. Also they provide a wider field of view as they are curved outwards.

Convex mirrors are used in some automated teller machines as a simple and handy security feature, allowing the users to see what is happening behind them. Similar devices are sold to be attached to ordinary computer monitors.

Some camera phones use convex mirrors to allow the user to correctly aim the camera while taking a self-portrait.

### Image

The image is always virtual (rays haven 't actually passed through the image,their extensions do), diminished (smaller), and upright . These features make convex mirrors very useful: everything appears smaller in the mirror, so they cover a wider field of view than a normal plane mirror does as the image is "compressed".

## Concave mirrors

A concave mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc.

A concave mirror, or converging mirror, has a reflecting surface that bulges inward (away from the incident light). Concave mirrors reflect light inward to one focal point, therefore they are used to focus light. Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror.

These mirrors are called "converging" because they tend to collect light that falls on them, refocusing parallel incoming rays toward a focus. This is because the light is reflected at different angles, since the normal to the surface differs with each spot on the mirror.

### Image

Effect on image of object 's position relative to mirror focal point (Concave)
Object 's position (S),
focal point (F)
Image Diagram
S < F
(Object between focal point and mirror)
• Virtual
• Upright
• Magnified (larger)
S = F
(Object at focal point)
• Reflected rays are parallel and never meet, so no image is formed.
• In the limit where S approaches F, the image distance approaches infinity, and the image can be either real or virtual and either upright or inverted depending on whether S approaches F from above or below.
F < S < 2F
(Object between focus and centre of curvature)
• Real
• Inverted (vertically)
• Magnified (larger)
S = 2F
(Object at centre of curvature)
• Real
• Inverted (vertically)
• Same size
• Image formed at centre of curvature
S > 2F
(Object beyond centre of curvature)
• Real
• Inverted (vertically)
• Reduced (diminished/smaller)

Posted by Prakhar Bindal(student), on 12/3/11

Hi Vineet!

The summary of image formed by concave and convex lenses is given below:

Convex lens:

Concave lens:

The summary of image formed by concave and convex mirrors is given below:

Concave mirror:

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