Statement-I : When an object dipped in a liquid is viewed normally, the distance between the image and the object is indepedent of the height of the liquid above the object.Statement-II : The normal shift is independent of the location of the slab between the object and the observer.a)Statement-1 is true, statement-2 is true; statement-2 is correct explanantion for satement-1b)Statement-1 is true, statement-2 is true; statement-2 is NOT correct explanantion for satement-1c)Statement-1 is true, Statement-2 is false.d)Statement-1 is false, statement-2 is true.Correct answer is option 'D'. Can you explain this answer?

Question

Answer

a) At first the height of the liquid level is obviously dependent because the normal shift will happen according to the depth of the liquid.
Drawing a ray diagram keeping a coin at very deep and another close to the surface.We will notice that the earlier one will have a noticeable change of position but the later one will only change a bit.
b) The position of the slab is independent because wherever we keep it the incident ray & the emergent ray at last will be parallel (same medium keeping in mind).

Answer

Statement-I : When an object dipped in a liquid is viewed normally, the distance between the image and the object is independent of the height of the liquid above the object.

Statement-II : The normal shift is independent of the location of the slab between the object and the observer.

Explanation:
Statement-I is related to the phenomenon of refraction of light. When an object is immersed in a liquid, the light rays coming from the object bend as they pass from one medium to another due to a change in their speed. This bending of light rays is known as refraction. Due to this refraction, an image of the object is formed which appears to be raised and closer to the surface of the liquid. The distance between the object and its image is given by the formula:

1/v - 1/u = 1/f

where v is the distance of the image from the surface of the liquid, u is the distance of the object from the surface of the liquid, and f is the focal length of the lens formed by the liquid. As per the statement, the distance between the image and the object is independent of the height of the liquid above the object. This is true because the height of the liquid above the object does not affect the refraction of light and hence does not affect the formation of the image.

Statement-II is related to the concept of normal shift. When light rays pass from one medium to another, they bend due to a change in their speed. The angle of incidence and angle of refraction are related by Snell's law:

n1sinθ1 = n2sinθ2

where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. The normal shift is the distance between the incident ray and the refracted ray measured along the normal to the surface of separation of the media. As per the statement, the normal shift is independent of the location of the slab between the object and the observer. This is false because the normal shift depends on the angle of incidence and angle of refraction which are affected by the location of the slab.

Hence, the correct option is D. Statement-I is false and Statement-II is true.

Answer

Look...

a) At first the height of the liquid level is obviously dependent because the normal shift will happen according to the depth of the liquid.

Draw ray diagrams keeping a coin at very deep and another close to the surface. You will notice that the earlier one will have a noticeable change of position but the later one wil only change a bit.

b) The position of the slab is independent because wherever you keep it the incident ray & the emervent ray at last will b parallel (same medium keeping in mind).

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