An object is placed in front of a concave mirror of focal length 12 cm. at a distance of 6 cm. Its image is formed at a distance of __________ and is _________.

Correct option is D

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Here’s the correct reasoning:

​$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$$​​

Where:

• f=−12 cm(focal length of the concave mirror; negative for concave),
• u=−6 cm (object distance; negative since the object is in front of the mirror),
• v is the image distance (to be calculated).

Substituting the values into the formula:

​$$\frac{1}{-12} = \frac{1}{v} + \frac{1}{-6}$$​​

Solving for vvv:

​$$\frac{1}{v} = \frac{1}{-12} + \frac{1}{6} = \frac{-1 + 2}{12} = \frac{1}{12}$$​​

Thus, v=+12 cm

Since the image distance v is positive, the image is formed on the same side as the object, indicating that the image is virtual and upright.

• Image distance: 12 cm.
• The image is virtual.

• Concave Mirror Behavior: When the object is placed between the focal point and the mirror (within the focal length), a concave mirror forms a virtual, upright, and magnified image.
• Virtual Images: These are formed when the rays appear to diverge from a point behind the mirror. They are upright and cannot be projected on a screen.