Two transparent slabs of thickness (t1, t2) and refractive index (μ1, μ2) are arranged one over another. An object is seen through this combination. Find equivalent refractive index ofthe system which will allow the image to be formed at the same place.

Question

Two transparent slabs of thickness (t1, t2) and refractive index (μ1, μ2) are arranged one over another. An object is seen through this combination. Find equivalent refractive index ofthe system which will allow the image to be formed at the same place. (A) ((t1+t2) μ1 μ2/t1 μ2+t2 μ1) (B) (t1+t2/μ1+μ2) (C) (t1 t2 μ1 μ2/(t1+t2)) (D) (t1 μ1/t2 μ2)

Tardigrade Admin · Accepted Answer

Correct answer is (a) ((t1+t2) μ1 μ2/t1 μ2+t2 μ1)

Q. Two transparent slabs of thickness $(t_{1}, t_{2})$ and refractive index $(μ_{1}, μ_{2})$ are arranged one over another. An object is seen through this combination. Find equivalent refractive index ofthe system which will allow the image to be formed at the same place.

$\frac{( t _{1} + t _{2} ) μ _{1} μ _{2}}{t _{1} μ _{2} + t _{2} μ _{1}}$

$\frac{t _{1} + t _{2}}{μ _{1} + μ _{2}}$

$\frac{t _{1} t _{2} μ _{1} μ _{2}}{( t _{1} + t _{2} )}$

$\frac{t _{1} μ _{1}}{t _{2} μ _{2}}$

Correct answer is (a) $\frac{( t _{1} + t _{2} ) μ _{1} μ _{2}}{t _{1} μ _{2} + t _{2} μ _{1}}$

Q. Two transparent slabs of thickness (t1​,t2​) and refractive index (μ1​,μ2​) are arranged one over another. An object is seen through this combination. Find equivalent refractive index ofthe system which will allow the image to be formed at the same place.

t1​μ2​+t2​μ1​(t1​+t2​)μ1​μ2​​

μ1​+μ2​t1​+t2​​

(t1​+t2​)t1​t2​μ1​μ2​​

t2​μ2​t1​μ1​​