(a) (i) "In refraction of light through a rectangular glass slab, the emergent ray is always parallel to the direction of the incident ray." Why? Explain with the help of a ray diagram. What happens when a ray of light falls normally on one of the faces of a rectangular glass prism? Draw diagram.

(ii) An object is placed at a distance of $30\ \mathrm{cm}$ from the optical centre of a concave lens of focal length $20\ \mathrm{cm}$. Use Lens formula to determine the position of the image formed in this case.

OR

(b) (i) A student wishes to study the image formation by a concave mirror using candle flame as object. State the type of the image formed by the mirror and mention the change in the image formed, if any, that he observes when the candle flame is gradually moved away from the pole of the mirror. Draw a ray diagram to show the image formation when the object distance is nearly equal to the radius of curvature of the mirror.

(ii) A convex mirror used for rear-view on an automobile has a focal length of $3\cdot 0\ \mathrm{m}$. If a bus is located at $6\cdot 0\ \mathrm{m}$ from this mirror, use mirror formula to find the position of the image of the bus as seen in the mirror.

(a)(i) Why the emergent ray is parallel to the incident ray, with ray diagram description

When a ray of light (AO) travelling in air strikes the first face of a rectangular glass slab obliquely at point O, it bends towards the normal (since it is entering an optically denser medium), travelling along OO′ inside the glass. At the second face, the same ray strikes the glass–air interface and bends away from the normal (leaving a denser medium for a rarer one), emerging along O′B. Because the two refracting surfaces of the slab are parallel, the angle of incidence at the first surface equals the angle of emergence at the second surface (this is proved using the fact that the normals at O and O′ are parallel, and applying Snell's law twice: $n_{ag}=\sin i/\sin r_1$ at the first surface and $n_{ga}=\sin r_1/\sin e$ at the second surface, so $n_{ag}\times n_{ga}=1$ gives $\sin i = \sin e$, i.e. $i=e$). Hence AO and O′B are parallel — the emergent ray is parallel to the incident ray, merely displaced sideways (laterally shifted) by a small amount depending on the slab's thickness and refractive index.

When a ray of light falls normally (perpendicular, i.e. angle of incidence $=0^\circ$) on one face of a rectangular glass prism, the angle of refraction is also $0^\circ$ (by Snell's law, since $\sin 0^\circ = 0$). The ray therefore passes straight through that first face without any bending and travels undeviated until it strikes the second, inclined face of the prism, where it bends as usual away from the normal on emerging into air. (A simple diagram would show a ray entering perpendicular to one face of a triangular prism, continuing straight inside without deviation, then bending at the slanted second face as it emerges.)

(a)(ii) See stepByStepSolution: the image is virtual, erect and diminished, formed $12\ \mathrm{cm}$ from the optical centre on the same side as the object — consistent with the chapter's description that a concave lens always produces a virtual, erect, diminished image located between the optical centre and the focus, for any real object position.

(b)(i) Concave mirror — image formation as the flame moves away from the pole

Using a concave mirror to study image formation with a candle flame (as in the chapter's Activity on concave mirrors, section 9.2), the following sequence is observed as the object distance $u$ is gradually increased (flame moved away from the pole):

• Object between pole and focus ($u<f$): image is virtual, erect and magnified (enlarged), formed behind the mirror.
• Object between $F$ and $C$ ($f<u<2f$, i.e. $f<u<R$): image is real, inverted and magnified (enlarged), formed beyond $C$.
• Object at $C$ (i.e. $u\approx R = 2f$): image is real, inverted and of the same size as the object, formed at $C$ itself.
• Object beyond $C$ ($u>2f$): image is real, inverted and diminished, formed between $F$ and $C$.
• Object at infinity: a real, inverted, highly diminished, point-sized image is formed at $F$.

So, as the flame is moved away from the pole, the image changes progressively from virtual–erect–magnified, to real–inverted–magnified, to real–inverted–same size (at $u\approx R$), and finally to real–inverted–diminished.

(b)(ii) See stepByStepSolution: the image of the bus is virtual, erect, diminished and located $2.0\ \mathrm{m}$ behind the convex mirror. This confirms why convex mirrors are used as rear-view/side mirrors on vehicles — as stated in the chapter, a convex mirror always forms a diminished, erect image, giving the driver a much wider field of view of traffic behind the vehicle than a plane mirror of the same size would.