Concept-
- The optical instrument which reflects the light and makes the image of the object is called a mirror.
- The mirror has a spherically curved reflecting surface is called a spherical mirror.
There are two types of spherical mirror:
1. Concave mirror:
- The spherical mirror having an inward reflecting surface is called a concave mirror.
- The images form by the concave mirror can be real as well as virtual.
2. Convex mirror:
- The mirror whose reflecting surface is outward is called a convex mirror.
- The images formed by the convex mirror is always virtual.
Mirror Formula: The following formula is known as the mirror formula, which provided a relation between focal length, image distance, and objects distant as shown below
f1=v1+u1
The following representation depicts the New Cartesian Sign Convention for spherical mirrors:
Where,
u = object distance, v = image distance, f = the focal length of the mirror
Focal length = R/2
Where R = radius of curvature of mirror.
- Magnification: In a concave mirror, the magnification is the ratio of the height of the image to the height of the object.
- When the image is real, the magnification will be negative because the real image is inverted.
- When the image is virtual, the magnification will be positive because the virtual image is erect.
m=u−v
Where m is magnificent, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.
Calculation:
Given: Radius of curvature = 20 cm
Focal length = R/2
f = 20/2 = 10 cm, by using sign: f = -10 cm.
For part AB and PB = 30 + 10 = 40 cm
u = -40 cm, from mirror formula
f1=v1+u1
−101=v1+−401
v1=−101−(−40)1=−403
v = - 13.3 cm.
So, PB’ = 13.3 cm
Magnification, m
m=u−v=−ABA′B′=−−40−13.3=−31
⇒ A’B’ = -10/3 = -3.33 cm
For part CD and PC = 30 cm, so, u = -30 cm.
v1=f1−u1
v1=−101−(−−301)=−151
v = -15 cm = PC’
Magnification m,
m=CDC′D′=−uv=−(−30−15)=−21
⇒ C’D’ = 5 cm
B’C’ = PC’ – PB’ = 15 – 13.3 = 1.7 cm
So, total length A’B’ + B’C’ + C’D’ = 3.3 + 1.7 + 5 = 10 cm
Total length = 10 cm