Optics TBR Problem number 21 from 52 Question exam

[nkafeel]

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Focal length and refraction.Problem number 21 from 52 Question in light and optics TBR book 2 of physics.

So if something travels from air to glass vs oil to glass...refraction occurs more in air to glass in comparison to oil to glass since oil and glass have very similar indexes of refraction. Im having trouble understanding and relating to the increasing and decreasing of focal lengths. is there a way to prove this? am i missing something.

I dont understand how if something refracts more its focal lenth decreses. or the other way around. Hope you can clarify this.

 

[AwayFromReality]

Suppose you have a lens. As light enters from one side of the lens it refracts and lands on the other side of the lens. If you increase the index of refraction of the lens it will bend the light more therefore the refracted light ray will now land closer to the lens (smaller focal length). If you decrease the index of refraction of the lens the lens will bend the light ray less and it will land further away from the lens (greater focal length).

For the question you're talking about you have to look at the medium surrounding the glass lens. If the medium around the lens has the same or similar index of refraction light will not bend as much therefore focal length will be greater. If the index of refraction of the medium is very different than the glass lens then the light will bend more therefore the focal length will be smaller (i.e the refracted light will land closer to the lens).