Question

with the help of ray diagram, show the formation of image of point object by refraction of light at a spherical surface separating two media of refractive index n1 and n2 (n2>n1) respectively. using this diagram derive the relation between n2/V - n1/U = n2-n1/R

Answer 1

Answer:

OM = u = object distance

MI = v =image distance

MC = R = radius of curvature

angle i = angle of incidence

angle r = angle of refraction

ON =incident ray

NI =refracted ray

NC = normal & n1 ,n2 are the refractive indices

From the figure with small angles

tan∠NOM=MNOM , tan ∠NCM=MNMC and tan∠NIM=MNMIin the triangle NOC ,∠i =exterior angle = sum of the interior opposite angle∠i=∠NOC+∠NCO=∠NOM+∠NOM=MNOM+MNMCSimilarly ∠NCM=∠CNI=∠CNI+∠NIM∠r=∠CNI=∠MCN−∠NIM=MNMC−MNMIFrom Snell's law , n1 sin i = n2 sin rFor small angles n1 i = n2 rSubstituting the values of i & r we get ,n1(MNOM+MNMC)=n2(MNMC−MNMI)⇒n1OM+n2MI=n2−n1MCApplying sign cnvention , OM=−u ,MI=v and MC=Rn1v−n2u=n2−n1R