Define normal shift. Obtain an expression for normal shift when an object in a denser medium is viewed from a rarer medium.

Explanation

The apparent shift in the position of the object kept in one medium and viewed normally through another medium.

OP = incident ray
PQ = refracted ray produced backwards meet ON at I.
NN. = normal
OI = normal shift
`/_RPO = i = ` angle of incidence = NPO
`/_ QPS =r=` angle of refraction = NIP
t = thickness of the optical medium.
` sin i = ( NP )/( OP )` [ From the `Delta NPO`]
`sin r = ( NP )/( IP )` [ From the `Delta NP]`
`n_(1) sin i = n _(2) sin r `
Here, `n_(1)= n , n_(2) = 1 `
`n = ( NP )/( OP) = 1 ( NP )/( IP )`
`n = ( NP )/( IP ) xx ( OP )/( NP) = ( OP )/( IP ) = ( ON )/(IN ) `
`:.` P is the point which is very close to N
`n = ( "real depth ")/( "apparent depth")`
Normal shift `= OI = ON -IN`
`= ON - ( ON )/( n )`
`NS = ON [ 1- (1)/( n )] =t [ 1- ( 1)/ (n ) ]`
Normal shift `= t [ 1- ( 1)/( n ) ]`