A concave mirror is used for image formation for different positions of an object. What inferences can be drawn about the following when an object is placed at a distance of $10\text{ cm}$ from the pole of a concave mirror of focal length $15\text{ cm}$ ?

(a) Position of the image

(b) Size of the image

(c) Nature of the image

Draw a labelled ray diagram to justify your inferences.

Q: How many marks does this question carry in CBSE Class 10 Science 2020?

This question carries 3 marks in the CBSE Class 10 Science 2020 examination.

Q: 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.

Q: What topic does this question cover in Science?

This question covers the topic "Image Formation by Concave Mirror" from CBSE Class 10 Science.

Q: What type of question is this in the CBSE Class 10 Science 2020 paper?

This is a Short Answer question from Section B in the CBSE Class 10 Science 2020 paper.

Light — Reflection and Refraction

Image Formation by Concave Mirror

Official Answer

When an object is placed at a distance of $10\text{ cm}$ from a concave mirror of focal length $15\text{ cm}$ , the object lies between the pole ( $P$ ) and the principal focus ( $F$ ) of the mirror (since $u < f$ ).

Based on the principles of reflection and Table 9.1 of the NCERT textbook, the inferences are:

(a) Position of the image: Behind the mirror (at a distance of $30\text{ cm}$ from the pole).

(b) Size of the image: Enlarged (magnified by a factor of $3$ ).

Ray Diagram:


                  M
                  |\ 
          A       | \     A'
\
\
    ------B-------P----F'-B'------ (Principal Axis)
         C   F    |  /
                  | / 
                  N/

	\
	\

(In this diagram, the object $AB$ is placed between $P$ and $F$ . Ray 1 parallel to the principal axis reflects through $F$ . Ray 2 passing through $C$ reflects back along $C$ . When produced backwards, these rays meet at $A'$ behind the mirror to form the virtual, erect, and enlarged image $A'B'$ .)

Behind the mirrorEnlargedVirtual and erectMirror formulaBetween P and F

Marking Scheme

1State that the object lies between the pole and focus of the concave mirror. (0.5 marks)
2Correctly calculate the image distance ( $v = +30\text{ cm}$ ) using the mirror formula. (1 mark)
3State the correct characteristics: Position (behind the mirror), Size (enlarged), and Nature (virtual and erect). (0.5 marks)
4Draw a neat, labelled ray diagram showing the object between $P$ and $F$ with virtual rays meeting behind the mirror. (1 mark)

Hint

Since the object distance ( $10\text{ cm}$ ) is less than the focal length ( $15\text{ cm}$ ), the object is between $P$ and $F$ . Use the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ to find the exact position and nature.

Quick Oral Answer

When an object is placed within the focal length of a concave mirror, it forms a virtual, erect, and magnified image behind the mirror because the reflected rays diverge in front and only appear to meet when extended backwards.

Analysis & Explanation

According to Table 9.1 of the NCERT textbook, when an object is placed between the pole ( $P$ ) and the focus ( $F$ ) of a concave mirror, the image is formed behind the mirror. This is the only position for a concave mirror where a virtual, erect, and magnified image is produced. This property makes concave mirrors highly useful as shaving mirrors or dentist mirrors, where a magnified and upright view of an object is required.

Common Mistakes

1Forgetting to apply the proper sign convention (e.g., taking $u$ as positive instead of negative).
2Drawing solid lines behind the mirror instead of dashed lines for virtual rays.
3Confusing the focal length of a concave mirror as positive.

Interesting Facts

This specific configuration is the only case where a concave mirror behaves like a magnifying glass, producing a virtual and erect image instead of a real and inverted one.

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Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2020?

This question carries 3 marks in the CBSE Class 10 Science 2020 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 Concave Mirror" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2020 paper?

This is a Short Answer question from Section B in the CBSE Class 10 Science 2020 paper.