For a convex mirror, the focal length is positive ($+f$).
- Object distance: $u = -f$
- Object height: $h_o = 1\,\text{m}$
Using the mirror formula:
$$\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \implies \frac{1}{v} - \frac{1}{f} = \frac{1}{f} \implies \frac{1}{v} = \frac{2}{f} \implies v = \frac{f}{2}$$
Linear magnification is:
$$m = -\frac{v}{u} = -\frac{f/2}{-f} = +\frac{1}{2} = 0.50$$
Height of the image:
$$h_i = m \times h_o = 0.50 \times 1\,\text{m} = 0.50\,\text{m}$$
Hence, option 4 is the correct answer.
उत्तल दर्पण के लिए फोकस दूरी धनात्मक होती है ($+f$):
- वस्तु की दूरी: $u = -f$
- वस्तु की ऊँचाई: $h_o = 1\,\text{m}$
दर्पण सूत्र से:
$$\frac{1}{v} + \frac{1}{-f} = \frac{1}{f} \implies \frac{1}{v} = \frac{2}{f} \implies v = \frac{f}{2}$$
आवर्धन:
$$m = -\frac{v}{u} = -\frac{f/2}{-f} = 0.50$$
प्रतिबिंब की ऊँचाई:
$$h_i = m \times h_o = 0.50 \times 1\,\text{m} = 0.50\,\text{m}$$
अतः विकल्प 4 सही उत्तर है।