Q4. Assertion: a magician’s glass lens (n = 1.47) vanishes in a trough of liquid of refractive index 1.47. Reason: when n21 = 1 the lens maker’s formula gives 1/f = 0, so the lens bends no light. Are both true, and does the reason explain the assertion?
Both hold in the ideal transparent, index-matched model at the observed wavelength; the liquid cannot be water (n = 1.33) but could be glycerine (NCERT Example 9.6, page 236).
Q5. The image of a bulb on one wall is to be cast on the opposite wall 3 m away with a convex lens. What is the largest focal length that will do?
A real image needs the object–image distance D to be at least 4f, so f ≤ D/4 = 0.75 m (NCERT Exercise 9.18, page 251; answer on page 347).
Q6. A screen is 90 cm from an object. A convex lens forms a sharp image on it at two positions 20 cm apart. Find its focal length.
Use positive distance magnitudes U and V: U + V = 90 cm and V − U = 20 cm, so V = 55 cm and U = 35 cm (Cartesian u = −35 cm, v = +55 cm). Then 1/f = 1/55 + 1/35 gives f ≈ 21.4 cm (NCERT Exercise 9.19, page 251; answer on page 347).
Q7. A beam converging to a point P meets a concave lens of focal length 16 cm placed 12 cm before P. Where does it converge now?
u = +12 cm (virtual object), f = −16 cm: 1/v = −1/16 + 1/12 = 1/48, so v = 48 cm to the right of the lens, a real image (NCERT Exercise 9.8(b), page 249; answer on page 346).