IIT JEE , AIEEE Forum - Physics , General - convex mirror, M=1/2 when placed at A, M=1/3 when placed at B, A-B=30cm,find f?

dwipayan.patnaik

light-reflection and refraction

dwipayan.patnaik

what is f?

karansingh

good afternoon, dwipayan !

here is the solution.

- v_a / u_a= 1 / 2

v_a = - u_a / 2 .........................eq 1

- v_b / u_b = 1 / 3

v_b = - u_b / 3 ..................................eq2

Now

1 / v_a+ 1 / u_a = 1 / v_b + 1 / u_b

replacing v_aand v_b from eq 1 and eq 2 and solving it we get,
u_b = 2 u_{a ................................}eq 3

u_a - u_b = 30
replacing u_b by eq 3,

u_a - 2 u_a = 30

u_a = - 30 ........................... eq 4

from eq 4 and eq 1,
we get v_a = 15 .................... eq 5

now by mirror formula,
1 / f = 1 / v_a + 1 / u_aplugging in eq 5 and eq 4,

f = { (1 / 15) + ( 1 / -30 ) }^-1= { 1 / 30 }^-1= 30 cm

so f = 30 cm

hope that my solution is correct.

PS - i am Karan, if u can recall.

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