Home
Class 12
PHYSICS
If incident ray, refracted ray and norma...

If incident ray, refracted ray and normal ray are represented by unit vectors `vec a, vec b ,and vec c` then relation between them is ?

A

` vec(b) = vec(a) + 2 vec(c )`

B

` vec(b) = 2 vec(a) + vec (c ) `

C

`vec(b) = vec(a) - 2 ( vec(a) * vec(c )) vec(c )`

D

` vec(b) = vec(a) - vec(c )`

Text Solution

Verified by Experts

The correct Answer is:
C

We see from the diagram that because of the law of reflection, the component of the unit vector ` vec (a) ` along ` vec (b)` changes sign on reflection while the component parallel to the mirror remain unchanged
`vec (a) = vec (a_(||)) + vec (a_(bot))`
And ` vec (a_(bot)) = vec (c) ( vec (a) . vec (c))`
We see that the reflected unit vector is
` vec (b) = vec(a_(||)) - vec (a_(bot)) rArr vec (a) - 2 ( vec (a ) . vec (c)) vec (c) `
Promotional Banner

Similar Questions

Explore conceptually related problems

If vec a,vec b,vec c are mutually perpendicular unit vectors,find |2vec a+vec b+vec c|

If vec a and vec b are two vectors such that (vec a+vec b)vec a-vec b=0 find the relation between the magnitudes of vec a and vec b

If two vectors vec a,vec b are such that |vec a*vec b|=|vec a xxvec b| then angle between them is

If the angel between unit vectors vec a and vec b60^(@) ,then find the value of |vec a-vec b|

If the incident ray on a surface is along the unit vector vec v ,the reflected ray is along the unit vector vec w and the normal is along the unit vector vec a outwards,express vec w in terms of vec a and vec v

If vec a,vec b, and vec c are non-zero vectors such that vec a.vec b=vec a*vec c, then find the geometrical relation between the vectors.

If vec a and vec b are unit vectors find the angle between vec a+vec b and vec a-vec b

The non-zero vectors vec a,vec b,vec c are related by vec a=8vec b and vec c=-7vec b then the angle between vec a&vec c