Question 24 of 29intermediate🔧 ApplyNumerical3 marks

An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Correct Answer

Object-distance, u = -10 cm (negative sign convention) Focal length, f = +15 cm (positive for convex mirror)

Using mirror formula: 1/v + 1/u = 1/f

1/v = 1/f - 1/u 1/v = 1/(+15) - 1/(-10) 1/v = 1/15 + 1/10 1/v = (2 + 3)/30 = 5/30 v = +6 cm

Magnification, m = -v/u = -6/(-10) = +0.6

Position of image: 6 cm behind the mirror.

Nature of image: The image is virtual, erect and diminished (smaller than the object).

Exercise: EXERCISES | Q: 12 | (Page Page 26)
For More Understanding

Explanation

This question tests the application of mirror formula for convex mirrors. Following the sign convention from Example 9.1 in the textbook, object distance is taken as negative and focal length is positive for convex mirrors. The positive value of v indicates the image is formed behind the mirror, making it virtual. The positive magnification (m = +0.6) confirms the image is erect, and since m < 1, the image is diminished.

Solution Steps

  1. Step 1: Identify given values - u = -10 cm, f = +15 cm

  2. Step 2: Apply mirror formula 1/v + 1/u = 1/f

  3. Step 3: Calculate v = +6 cm

  4. Step 4: Calculate magnification m = -v/u = +0.6

  5. Step 5: Interpret results - image is virtual, erect and diminished

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