According to the New Cartesian Sign Convention, which one of the following is correct in respect of the formula 1/f = 1/v + 1/u, where symbols have their usual meanings?
- (a)It applies only to spherical mirrors.
- (b)It applies only to spherical lenses.
- (c)It applies to spherical mirrors as well as spherical lenses.
- (d)It is an invalid formula.
Correct — A, it applies only to spherical mirrors. Under the New Cartesian Sign Convention, the mirror formula is 1/f = 1/v + 1/u (with a plus sign), while the thin-lens formula is 1/f = 1/v – 1/u (with a minus sign). Because the given relation uses the plus sign, it is the mirror formula and holds for spherical mirrors, not lenses.
- (b)It applies only to spherical lenses. — The lens formula is 1/f = 1/v – 1/u (minus sign); the plus-sign form given here is not the lens formula.
- (c)It applies to spherical mirrors as well as spherical lenses. — The two devices have different formulas — plus for mirrors, minus for lenses — so a single plus-sign relation cannot serve both.
- (d)It is an invalid formula. — It is perfectly valid — it is the standard mirror formula under the New Cartesian Sign Convention.
The New Cartesian Sign Convention fixes signs for distances measured from the pole (mirror) or optical centre (lens): distances measured against the incident light are negative, those along it positive; heights above the axis are positive. With these conventions the mirror formula is 1/f = 1/v + 1/u and the lens formula is 1/f = 1/v – 1/u, where u, v and f are object distance, image distance and focal length.
The single sign is the whole trap. The two formulas look almost identical, so the plus versus minus is the deciding clue. Spotting '+u' tells you it is the mirror relation; a '–u' would be the lens relation. Recognising this immediately rules out the lens and 'both' options.
- Mirror formula (New Cartesian): 1/f = 1/v + 1/u.
- Thin-lens formula (New Cartesian): 1/f = 1/v – 1/u.
- For a spherical mirror, focal length f = R/2, where R is the radius of curvature.
- Magnification: m = –v/u for mirrors and m = v/u for thin lenses.
The '+' in front of 1/u marks the relation as the mirror formula, so it applies only to spherical mirrors.
- Confusing the mirror formula (+ sign) with the lens formula (– sign).
- Forgetting to apply sign conventions when substituting u, v and f.
Asked by giving a formula and asking which device it applies to, or by testing the sign difference between mirror and lens relations.
No directly related past PYQ was found.
- practice — not a real PYQ
Under the New Cartesian Sign Convention, the thin-lens formula is
- (a)1/f = 1/v + 1/u
- (b)1/f = 1/v – 1/u
- (c)f = 2R
- (d)1/f = u + v
Answer(b) 1/f = 1/v – 1/u — the lens formula uses a minus sign.
- practice — not a real PYQ
For a spherical mirror, the focal length f and radius of curvature R are related by
- (a)f = R
- (b)f = 2R
- (c)f = R/2
- (d)f = R/4
Answer(c) f = R/2 — the focal length is half the radius of curvature.