Q4. Use the mirror equation to show that an object placed between f and 2f of a concave mirror gives a real image beyond 2f.
For a concave mirror f and u are negative, so 1/v = 1/f − 1/u = 1/|u| − 1/|f|. With |f| < |u| < 2|f|, this is negative but smaller in size than 1/(2|f|). So v is negative, a real image in front of the mirror, and |v| > 2|f| (NCERT Exercise 9.15(a), page 250).
Q5. Show that an object between the pole and the focus of a concave mirror gives a virtual, enlarged image.
With |u| < |f|, 1/v = 1/f − 1/u = 1/|u| − 1/|f| > 0, so v is positive: a virtual image behind the mirror. Then v = |u||f|/(|f| − |u|) > |u|, so m = −v/u > 1: erect and enlarged (NCERT Exercise 9.15(d), page 250).
Q6. Assertion: a car approaching at a steady speed seems to speed up in a convex side-view mirror. Reason: the image distance v = fu/(u − f) changes faster as the car comes closer. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: NCERT Example 9.4 finds the image speed rising from 1/280 m/s to 1/10 m/s as the distance falls from 39 m to 9 m (NCERT pages 227–228).
Q7. An object is 30 cm in front of a convex mirror of focal length 20 cm. Find the image distance and the magnification.
v = fu/(u − f) = 20 × (−30)/(−30 − 20) = +12 cm, behind the mirror; m = −v/u = 0.4: virtual, erect and smaller (NCERT Eqs. (9.7) and (9.9), pages 225–226).