Optics Concept Page - 8

Definition

Images formed by spherical mirrors for object placed at different distances

When a object is placed far from the concave mirror it will form the real, diminished and inverted image of object on screen as shown in 1st diagram.
When a object is placed near the concave mirror it will form the real,magnified and inverted image of object on screen as shown in 2nd diagram.

Result

Describe the characteristics of the images formed by concave mirror for different object locations.

Result

Describe the characteristics of the images formed by convex mirror for different object locations.

Diagram

Ray diagram of image formation by spherical mirrors

Image shows the ray diagram for various positions of the object for concave and convex mirrors.

Diagram

Image formed by concave and convex mirror

The diagram presented below in figure illustrates the reflection patterns obtained from both concave and convex mirrors. The concave mirror on the left has a reflecting surface that curves inwards that resembles a portion of the interior of a sphere. When light rays that are parallel to the principal, or optical axis, reflect from the surface of a concave mirror, in this case, the rays leading from the soldier's hat and feet, they converge on the focal point in front of the mirror. The distance from the reflecting surface to the focal point is termed the mirror's focal length. The size of the image depends upon the distance of the object from the mirror and it's position with respect to the mirror's surface. In this case, the soldier is placed at the center of curvature and the reflected image is upside down and in front of the mirror's center of curvature.
The convex mirror on the right-hand side of figure, however, has a reflecting surface that curves outward, which resembles a portion of the exterior of a sphere. Light rays parallel to the optical or principal axis are reflected from the surface in a manner that diverges from a focal point that is behind the mirror. Images formed with convex mirrors are always right side up and reduced in size. These images are also termed virtual images because when they occur reflected rays appear to diverge from a focal point behind the mirror.

Diagram

Image formation by spherical mirrors

Concave mirror	Object position	Image position	Image size	Image nature
1	Infinity	Focus	Point-sized	Real, inverted
2	Beyond C	Between C and F	Diminished	Real, inverted
3	At C	At C	Same size	Real, inverted
4	Between C and F	Beyond C	Magnified	Real, inverted
5	At F	infinity	Highly magnified	Real, inverted
6	Between F and P	Behind the mirror	Magnified	Virtual, erect

For convex mirror, image is always formed behind the mirror, virtual, erect and diminished.

Formula

Mirror formula

Mirror formula is an expression relating the image distance (v$v$), object distance (u$u$) and the focal length (f$f$).
1v+1u=1f${\displaystyle \frac{1}{v}}+{\displaystyle \frac{1}{u}}={\displaystyle \frac{1}{f}}$
Note:

• Utmost care should be taken regarding sign convention while using mirror formula.
• Focal length of convex mirror is taken as positive and concave mirror as negative.

Diagram

Plot of object distance vs image distance for spherical mirrors

as for mirror formula

1u+1v=1f${\displaystyle \frac{1}{u}}+{\displaystyle \frac{1}{v}}={\displaystyle \frac{1}{f}}$

and f is constant.

The relation between 1u${\displaystyle \frac{1}{u}}$ and 1v${\displaystyle \frac{1}{v}}$ is a linear relation, and

For a convex lens
1v−1u=1f${\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}={\displaystyle \frac{1}{f}}$

u−vvu=1f${\displaystyle \frac{u-v}{vu}}=\frac{1}{f}$

(vu)(u−v)=f${\displaystyle \frac{(vu)}{(u-v)}}=f$

The above equation looks like a hyperbola. Hence correct answer is A as negative u gives positive v.

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