# Aniket's Optics Challenges (Part 1)

Take a beaker as shown in the figure above with it's lower surface silvered so that base can act as a plane mirror . Now, pour liquids with different refractive index one above the other as shown in the above figure. Now place 2 similar lenses one on the base of the beaker and let the other float on the uppermost liquid. Now, place an object symmetrically at a distance of $$10\text{ cm}$$ from the upper layer of uppermost liquid.

Let an observer see the image of the object at a distance $$x$$ from the upper layer of topmost liquid .

The value of $$x$$ can be expressed as $$- \frac{a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers .

Enter your answer as $$a + b$$

Details and Assumptions :

• Consider only the paraxial rays.

• In figure the upper curved surface of lens has radius of curvature $${R}_{1} = 10 cm$$ and lower surface of lens has radius of curvature $${R}_{2} = 20 cm$$ and and refractive index is $$\mu = 1.5$$

• Refer to figure for information. The base of beaker act as a plane mirror .

• Lens are very thin (negligible small) .

• The distance $$x$$ is measured taking direction above liquid to be positive and is measured from upper layer of topmost liquid.

• Observer is observing from air ($$\mu = 1$$ ), symmetrically (i.e. on Principle axis).

• Lens are similar in context to optics , that is same refractive index and same geometry.

Hint : The light rays will go into the beaker then get reflected and then will come back again and the observer will see the resultant image.

As usual , It is Original. :)

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