Chapter 4: Problem 25

The image distance in case of a convex mirror can be (1) greater than focal length (2) less than focal length (3) equal to focal length (4) Both (2) and (3)

Short Answer

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Question: In the case of a convex mirror, the image distance can be: (a) Greater than the focal length (b) Less than the focal length (c) Equal to the focal length (d) A combination of (a), (b), and (c) Answer: (b) Less than the focal length Explanation: In a convex mirror, the focal length is positive, and the object distance is negative. Using the mirror formula (1/f = 1/u + 1/v), we have deduced that the image distance (v) is always less than the focal length (f) in the case of a convex mirror. Hence, the correct option is (2) less than the focal length.

Step by step solution

Understand Mirror Formula and Convex Mirror Properties

In order to understand image distance in relation to the focal length of a convex mirror, we need to look at the mirror formula: 1/f = 1/u + 1/v where f is the focal length, u is the object distance, and v is the image distance. Note that all measurements are taken from the pole of the mirror. For a convex mirror, the focal length (f) is positive, and since the object is always placed in front of the mirror, the object distance (u) is negative.

Analyze Image Distance using the Formula

Using the mirror formula, we can determine the image distance (v) for a given object distance (u) and focal length (f) as follows: 1/v = 1/f - 1/u In the case of a convex mirror with a positive focal length (f) and negative object distance (u), the term 1/f is positive and -1/u is less negative. As such, when adding 1/f and (-1/u), we will get a positive value for 1/v. This means that the image distance (v) will also be positive.

Compare Image Distance with Focal Length

To deduce whether the image distance is greater than, less than, or equal to the focal length, we will compare the value of 1/v to that of 1/f. Since in a convex mirror 1/f is positive, and -1/u is less negative, we can conclude that: 1/v > 1/f By taking the reciprocal of both sides: v < f So, the image distance (v) in case of a convex mirror is always less than the focal length (f).

Answer the Question

From our analysis, we can conclude that the correct option among the given choices is: (2) less than the focal length

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The image distance in case of a convex mirror can be (1) greater than focal length (2) less than focal length (3) equal to focal length (4) Both (2) and (3)

Short Answer

Step by step solution

Understand Mirror Formula and Convex Mirror Properties

Analyze Image Distance using the Formula

Compare Image Distance with Focal Length

Answer the Question

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