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  • A convex mirror is placed on a stand, and an object is placed at a distance of  in front of it. The obser

A convex mirror is placed on a stand, and an object is placed at a distance of d=20 cm in front of it. The observer looks at the object’s image formed by the mirror, which appears to be at a distance D=-15 cm behind the mirror. When the observer shifts x=5 cm distance to the right, the apparent position of the image shifts by X=3 cm distance to the left. Determine the focal length f of the convex mirror using the parallax method.

Option: 1

0.7 cm


Option: 2

1.2 cm


Option: 3

0.6 cm


Option: 4

2.4 cm


Answers (1)

best_answer

Step 1: In the parallax method, the observer shifts and measures the apparent shift of the image when looking at it from different angles.
Given: Object distance (d)=20 cm Apparent image distance (D)=-15 cm Shift of observer (x)=5 cm Shift of apparent image (X)=3 cm Focal length of the convex mirror (f)=f
Step 2: Use the formula for the magnification (m) of the mirror to relate the object and image distances.

            m=-\frac{D}{d}

Step 3: Use the formula for magnification (m) in terms of the focal length (f) and object distance (d).

            m=-\frac{f}{d}

Step 4: Equate the two expressions for magnification (m) and solve for the focal length (f).

            -\frac{D}{d}=-\frac{f}{d}

            D=f

Step 5: Use the formula for parallax to relate the shift of observer (x), shift of apparent image (X), and the object and image distances.

            x=\frac{X}{D-f}

Step 6: Substitute the value of D from step 4 into the parallax formula.

            x=\frac{X}{f}

Step 7: Solve for the focal length (f).

            f=\frac{X}{x}=\frac{3 cm}{5 cm}=0.6 cm

So, the focal length (f) of the convex mirror is 0.6 cm.
Therefore, the correct answer C.

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