चित्रानुसार प्रदर्शित गोले पर आवेश है

Options

A. `n_(1)=n_(2)=n_(3)`
B. `n_(1)=n_(2)!=n_(3)`
C. `1+n_(1)=n_(2)+n_(3)`
D. `1+n_(2)^(2)=n_(1)^(2)+n_(3)^(2)`

Answer

D

Explanation

`alpha=90^(@)-r_(1),beta=90^(@)-r_(2),gamma=90^(@)-r_(3)`
B पर
`sin i=n_(1)sin r_(1)impliessin^(2)i=n_(1)^(2)sin^(2)r_(1)`…………..(i)
C पर
`n_(1)sin (90^(@)-r_(1))=n_(2)sin r_(2)` `impliesn_(2)^(2)sin^(2)r_(2)=n_(1)^(2)cos^(2)r_(1)`...........ii
D पर
`n_(2)sin(90^(@)-r_(2))=n_(3) sin r_(3)`
`implies n_(2)^(2)cos^(2)r_(2)=n_(3)^(2)sin^(2)r_(3)`.........(iii)
E पर
`n_(3)sin (90^(@)-r_(3))-(1)sin (90^(@)-i)`
`impliescos^(2)i=n_(3)^(2)cos^(2)r_(3)`......iv
समी (i), (ii) , (iii) एवं (iv) को जोड़ने पर
`1+n_(2)^(2)=n_(1)^(2)+n_(3)^(2)`