Figure -18-Q3- shows three transparent media of refractive indices -956-1- -160- -956-2 -160-and -160- -956-3- A point object O is placed in the medium -956-2- If the entire medium on the right of the spherical surface has refractive index -956-1- the image forms at O -39- If this entire medium has refractive index -956-3- the image forms at O quot- In the situation shown-a- the image forms between O -39- and O quot-b- the image forms to the left of O -39-c- the image forms to the right of O quot-d- two images form- one at O -39- and the other at O quot-Figure

(d) two images form, one at O #39; and the other at O quot;Light will be refracted differently in both mediums on the right side. Thus, two images will be f ...

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Standard XII

Physics

Optical Path Length

Figure (18-Q3...

Question

Figure (18-Q3) shows three transparent media of refractive indices $μ_{1}, μ_{2} and μ_{3}$ . A point object O is placed in the medium $μ_{2}$ . If the entire medium on the right of the spherical surface has refractive index $μ_{1}$ , the image forms at O'. If this entire medium has refractive index $μ_{3}$ , the image forms at O". In the situation shown,
(a) the image forms between O' and O"
(b) the image forms to the left of O'
(c) the image forms to the right of O"
(d) two images form, one at O' and the other at O".
Figure

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Solution

(d) two images form, one at O' and the other at O"

Light will be refracted differently in both mediums on the right side. Thus, two images will be formed, one at O' due to refraction from medium μ₁ and another at O" due to refraction from medium μ₃.μ1

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Q. Figure (18-Q3) shows three transparent media of refractive indices

μ_{1}, μ_{2} and μ_{3}

. A point object O is placed in the medium

μ_{2}

. If the entire medium on the right of the spherical surface has refractive index

μ_{1}

, the image forms at O'. If this entire medium has refractive index

μ_{3}

, the image forms at O". In the situation shown,
(a) the image forms between O' and O"
(b) the image forms to the left of O'
(c) the image forms to the right of O"
(d) two images form, one at O' and the other at O".
Figure

Q. (a) Derive the mathematical relation between refractive indices

n_{1}

and

n_{2}

of two media and radius of curvature R for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index

n_{1}

and a real image formed in the denser medium of refractive index

n_{2}

. Hence, derive Lens Maker's formula.

(b) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed ?

In the adjoining figure, SS is a spherical surface separating two media of refractive indices n₁ and n₂ where n₁ > n₂. C is the centre of curvature of the spherical surface. An observer, keeping his eye beyond C in the medium of refractive index n₂ views the refracted image of an object AB placed as shown in the medium of refractive index n₁. The image will be:

Q. A thin lens made of a material of refractive index μ₂ has a medium of refractive index μ₁ on one side and a medium of refractive index μ₃ on the other side. The lens is biconvex and the two radii of curvature have equal magnitude R. A beam of light travelling parallel to the principal axis is incident on the lens. Where will the image be formed if the beam is incident from (a) the medium μ₁and (b) from the medium μ₃?

Q. Where would an object be placed in a medium of refractive index

μ_{1}

, so that its real image is formed at equidistant from sphere (of radius R and refractive index

μ_{2}

) which is also placed in the medium of refractive index

μ_{1}

as shown in figure?

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(d) two images form, one at O' and the other at O"Light will be refracted differently in both mediums on the right side. Thus, two images will be formed, one at O' due to refraction from medium μ1 and another at O" due to refraction from medium μ3.μ1

(d) two images form, one at O' and the other at O"

Light will be refracted differently in both mediums on the right side. Thus, two images will be formed, one at O' due to refraction from medium μ₁ and another at O" due to refraction from medium μ₃.μ1