Table of contents  
What is Reflection?  
Laws of Reflection  
Types of Reflection  
Image Formation by a Plane Mirror  
Mirror Equation  
Sign Conventions 
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There are majorly two types of reflection:
(i) Specular/Regular reflection
(ii) Diffused/Irregular reflection
Characteristics of Images formed by Plane Mirror
(i) Images formed by a plane mirror are “Always Virtual”.
(ii) Images formed by a plane mirror are “Erect/Upright”.
(iii) Images formed by a plane mirror are of the “same shape and size” as that of an object.
a. Find the angle of incidence.
b. Find the angle of reflection.
c. Find the angle made by the reflected ray and the surface.
d. Find the angle made by the incident and reflected rays.
Sol: We’ll use the diagram given below to answer the question:
Ans: a. Angle of Incidence (Q_{i})= 90^{0}42^{0}= 48^{0}
b. Angle of Reflection (Q_{r})= (Q_{i})= 48^{0}
c. x = 90^{0}Q_{r} = 90^{0}48^{0} = 42^{0}
d. Q_{i} + Q_{r} = 48^{0} + 48^{0} = 96^{0}
Ques 2: If the distance of an object and its virtual image from the focus of a convex lens of focal length f are 1 cm each, then f is
(a) 4 cm
(b) (√2+1) cm
(c) 2√2 cm
(d) (2+√2) cm
Sol:
Here, u = – (f – 1)
v = – (f + 1)
f = + f
Applying 1/v – 1/u = 1/f, we have
[1/(f+1)] + [1/(f –1)] = 1/f
Or, f2 – 2f – 1 = 0
This gives f = (√2+1) cm
From the above observation, we conclude that, option (b) is correct.
Ques 3: A transparent rod 40 cm long is cut flat at one end and rounded to a hemispherical surface of 12 cm radius at the other end. A small object is embedded within the rod along its axis and halfway between its ends. When viewed from the flat end of the rod, the object appears 12.5 cm deep. What is its apparent depth when viewed from the curved end?
Sol:
For the flat surface:
The flat surfaceReal depth of the object = 20 cm
Apparent depth = 12.5 cm
Using m = real depth / apparent depth
m = 20 / 12.5 = 1.6
For the curved surface:
The curved surfaceWe will use, (m1/u) + (m2/v) = m2  m1/R
u = 20 cm, R = 12 cm
So, (1.6/20) + (1/v) = (1 1.6)/(12)
Or, 1/v = (1/20) – (1.6/20)
Or, v = 33.3 cm
Hence the object appears 33.3 cm deep from the curved side.
It is an equation relating object distance and image distance with focal length that is known as a mirror equation. It is also known as a mirror formula.
In a spherical mirror:
In ray optics, The object distance, image distance, and Focal length are related as,
Where,
u is the Object distance
v is the Image distance
f is the Focal Length given by f=R2
R is the radius of curvature of the spherical mirror
The above formula is valid under all situations for all types of spherical mirrors (Concave and Convex) and for all object positions.
New Cartesian Sign Convention is used to avoid confusion in understanding the ray directions. Refer to the diagram for clear visualization.
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157 videos452 docs213 tests
