A glass slab of known thickness is placed on a horizontal platform. A traveling microscope is set up in such a way that it views the image of a distant object through the glass slab. The microscope is focused on the image without the glass slab. When the glass slab is placed, the microscope needs to be moved vertically upward by
to focus on the image again. Determine the refractive index
of the glass slab.
Step 1: The situation involves the glass slab acting as a medium with a certain refractive index through which light passes.
Step 2: Consider the setup. When the microscope is focused on the distant object without the glass slab, the light travels through air (with refractive index ).
Step 3: When the glass slab is placed on the platform, light travels through the glass slab (with refractive index ) and then through air.
Step 4: By Snell's Law, we have:
where is the angle of incidence and
is the angle of refraction inside the glass slab.
Step 5: Since , we get:
Step 6: When the microscope is moved vertically upward by units, the light ray gets displaced by
as well. The triangle formed by the displacement
, thickness of the glass slab
, and the angle of refraction
is a right-angled triangle.
Step 7: Using trigonometry, we have:
Step 8: Substitute the value of in terms of
and
into the equation from step 5:
Step 9: Solve for :
So, the refractive index of the glass slab is
.
So, option B is correct.
Study 40% syllabus and score up to 100% marks in JEE
5 g of Na2SO4 was dissolved in x g of H2O. The change in freezing point was found to be 3.820C. If Na2SO4 is 81.5% ionised, the value of x (K
A capacitor is made of two square plates each of side 'a' making a very small angle
A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of NaHCO3 to give fraction A. The leftover organic phase was extracted with d