Draw the ray diagram and also state the position, the relative size and the nature of image formed by a concave mirror when the object is placed at the centre of curvature of the mirror.
Draw the ray diagram and also state the position, the relative size and the nature of image formed by a concave mirror when the object is placed at the centre of curvature of the mirror.
When the object is placed at the centre of curvature (C) of a concave mirror, the image is formed at C itself, of the same size as the object, real and inverted.
Ray diagram (description):
- A ray from the top of the object travels parallel to the principal axis; after reflection from the concave mirror, it passes through the principal focus F.
- Another ray from the top of the object passes through the principal focus F; after reflection, it emerges parallel to the principal axis.
- The two reflected rays meet at a point on the principal axis exactly at the position of C (i.e., at a distance R = 2f from the pole).
- The image is formed at the centre of curvature C, is of the same size as the object, and is real and inverted.
Marking Scheme
- 11 mark for drawing the principal axis, mirror, pole, focus, and centre of curvature correctly with the object at C.
- 21 mark for drawing the two incident rays and their reflected rays correctly.
- 31 mark for stating the position (at C), relative size (same as object) and nature (real and inverted) of the image.
Hint
Remember that a ray directed towards the centre of curvature of a concave mirror is reflected back along the same path. Use this along with the ray parallel to the principal axis to locate the image.
Quick Oral Answer
When the object is placed at the centre of curvature of a concave mirror, the image is formed at the centre of curvature itself, is of the same size as the object, and is real and inverted.
Analysis & Explanation
For a concave mirror, the principal focus F lies midway between the pole P and the centre of curvature C. A ray passing through C is incident along the normal to the mirror, so it retraces its path. The other ray, parallel to the principal axis, converges at F after reflection. The two reflected rays meet at C itself, producing an image that coincides with the position of the object. Hence the image is real, inverted, and of the same size as the object. This is a standard case and is listed in Table 9.1 of the NCERT chapter.
Common Mistakes
- 1Drawing the image behind the mirror (virtual) instead of at C in front of the mirror.
- 2Marking the image as enlarged or diminished instead of the same size.
- 3Forgetting that a ray through C retraces its path and drawing it incorrectly.
Interesting Facts
The same result can also be obtained using the mirror formula: when u = −2f (object at C), v = −2f and magnification m = −1, confirming image is at C, real, inverted and same size.
This principle is used in reflecting telescopes where an object placed at C of the primary mirror produces an image of the same size at C, which is then magnified by a secondary mirror.
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Frequently Asked Questions
How many marks does this question carry in CBSE Class 10 Science 2011?
This question carries 3 marks in the CBSE Class 10 Science 2011 examination.
Which chapter does this question come from in Science?
This question is from the chapter "Light — Reflection and Refraction" in the CBSE Class 10 Science syllabus.
What topic does this question cover in Science?
This question covers the topic "Image formation by a concave mirror — object at the centre of curvature (C)" from CBSE Class 10 Science.
What type of question is this in the CBSE Class 10 Science 2011 paper?
This is a Short Answer question from Section A in the CBSE Class 10 Science 2011 paper.