Light - Refraction and Lenses PYQs – Physics, SSC & Railway

Formula — refractive index.
Refractive index = speed of light in vacuum ÷ speed of light in the medium
n = c ÷ v ⇒ v = c ÷ n
Substitute.
c = 3 × 10^(8) m/s, n = 1.33
v = 3 × 10^(8) ÷ 1.33
= 2.26 × 10^(8) m/s
Answer: 2.26 × 10^(8) m/s
Revision note — Refractive index and speed of light
• Light is fastest in vacuum (3 × 10^(8) m/s); every medium has n > 1.
• Speeds: water (n = 1.33) about 2.25 × 10^(8) m/s; glass (n = 1.5) 2 × 10^(8) m/s; diamond (n = 2.42) about 1.24 × 10^(8) m/s.
• Higher n ⇒ optically denser ⇒ slower light.
• On refraction the speed and wavelength change, but the frequency stays the same.
Any answer above 3 × 10^(8) m/s is impossible — light can never travel faster in water than in vacuum.
Also asked from this topic: the speed of light in glass of refractive index 1.5 (2 × 10^(8) m/s); the property of light that does not change on refraction (frequency).

Answer: Option 3 — They are equidistant from the optical centre.
A thin lens with equally curved faces has its two centres of curvature, C_(1) and C_(2), on the principal axis, one on each side, at the same distance from the optical centre O.
Revision note — Spherical lens terms
• Centre of curvature (C): centre of the sphere of which a lens surface is a part; a lens has two (C_(1), C_(2)).
• Optical centre (O): the central point of the lens; a ray through it passes undeviated.
• Principal axis: the line through both centres of curvature and O.
• Principal focus (F): a lens has two foci, F_(1) and F_(2); the distance OF is the focal length f.
• For a thin lens, the points at 2F_(1) and 2F_(2) are used as the centres of curvature in ray diagrams (radius R = 2f).
• All lens distances are measured from the optical centre.
Do not mix these up
• Lens vs mirror — a mirror has one centre of curvature and one focus; a lens has two of each.
Also asked from this topic: the path of a ray through the optical centre of a thin lens (continues without deviation); the point from which lens distances are measured (the optical centre).

Answer: Option 3 — When the object is placed at twice the focal length
For a convex lens, an object at 2F₁ gives an image at 2F₂.
The image is real, inverted and of the same size — magnification m = −1, i.e. size ratio exactly 1.
Revision note — Image formation by a convex lens
• Object at infinity → image at F₂, highly diminished, real, inverted.
• Object beyond 2F₁ → image between F₂ and 2F₂, diminished, real, inverted.
• Object at 2F₁ → image at 2F₂, same size, real, inverted.
• Object between F₁ and 2F₁ → image beyond 2F₂, enlarged, real, inverted.
• Object at F₁ → image at infinity, highly enlarged.
• Object between F₁ and O → image on the same side, virtual, erect, enlarged — the magnifying glass.
• Magnification m = v/u = h′/h; a negative m means real and inverted, positive means virtual and erect.
Do not mix these up
• m = −1 vs m = +1 — −1 is a real, inverted, same-size image (object at 2F); +1 is what a plane mirror gives (virtual, erect, same size).
Also asked from this topic: where the image forms when the object is at 2F₁ of a convex lens (at 2F₂); where to place the object for a real image twice its size (between F and 2F).