Point object O is as shown in diagram. At distance (x) an object is placed such that its final image coincides with it. For this the value of x are n 1 and n 2 then find the value of 15 n 1 + n

Question

Point object O is as shown in diagram. At distance (x) an object is placed such that its final image coincides with it. For this the value of x are n 1 ​ and n 2 ​ then find the value of 15 n 1 ​ + n 2 ​ ​ .

TestHub · Accepted Answer

For the final image to coincide with the object, the rays must retrace after reflection at the mirror.

Case 1: $\frac{1}{15} - \frac{1}{- x} = \frac{1}{10}$ gives $x = 30$ cm. Case 2: $\frac{1}{30} - \frac{1}{- x} = \frac{1}{10}$ gives $x = 15$ cm.

$\frac{n _{1} + n _{2}}{15} = \frac{30 + 15}{15} = 3$ .

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