Question 394 marksSection E

Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors:

CaseMirrorFocal Length (cm)Object Distance (cm)
1A2045
2B1530
3C3020

(i) In which one of the above cases the mirror will form a diminished image of the object? Justify your answer. (ii) List two properties of the image formed in case 2. (iii) (A) What is the nature and size of the image formed by mirror C? Draw ray diagram to justify your answer. OR (iii) (B) An object is placed at a distance of 18cm18\mathrm{cm} from the pole of a concave mirror of focal length 12cm12\mathrm{cm} . Find the position of the image formed in this case.

Chemical Reactions and Equations
Spherical Mirrors - Concave Mirror

Official answer

(i) Case 1 (Mirror A) will form a diminished image. Justification: Here, f=20 cmf = 20\text{ cm}, so C=2f=40 cmC = 2f = 40\text{ cm}. Since the object distance u=45 cmu = 45\text{ cm} is greater than 2f2f (u>Cu > C), the object is placed beyond the Centre of Curvature. For a concave mirror, an object beyond CC forms a diminished image between FF and CC.

(ii) In Case 2, f=15 cmf = 15\text{ cm} and u=30 cmu = 30\text{ cm}. Since u=2fu = 2f, the object is at the Centre of Curvature (CC). Properties: 1. The image is real and inverted. 2. The image is of the same size as the object.

(iii) (A) For Mirror C, f=30 cmf = 30\text{ cm} and u=20 cmu = 20\text{ cm}. Since u<fu < f, the object is between the Pole (PP) and Focus (FF). Nature: Virtual and erect. Size: Highly enlarged (magnified).


OR

(iii) (B) Given: u=−18 cmu = -18\text{ cm}, f=−12 cmf = -12\text{ cm}.

Using mirror formula: 1v+1u=1f\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

1v=1−12−1−18=−3+236=−136\frac{1}{v} = \frac{1}{-12} - \frac{1}{-18} = \frac{-3 + 2}{36} = -\frac{1}{36}

v=−36 cmv = -36\text{ cm}.

The image is formed at a distance of 36 cm36\text{ cm} in front of the mirror.

Answer keywords:Concave mirrorDiminishedReal and invertedVirtual and erectMirror formulaFocal lengthMagnified

Marking scheme

  1. 1.Identification of Case 1 with justification (u>2fu > 2f) (1 mark)
  2. 2.Two properties for Case 2 (Real/Inverted, Same size) (1 mark)
  3. 3.Nature/Size for Mirror C and Ray Diagram (A) OR Mirror formula calculation for v (B) (2 marks)

Hint

Always use the sign convention: uu and ff are negative for a concave mirror in real-image cases.

Quick oral answer

For a concave mirror, if the object is beyond C, the image is diminished. If it's at C, the image is the same size. If it's between P and F, the image is virtual, erect, and magnified. The mirror formula 1/v+1/u=1/f1/v + 1/u = 1/f helps calculate the exact position.

Common mistakes

  1. 1.Forgetting the negative sign for focal length of a concave mirror.
  2. 2.Confusing the object position for a diminished vs magnified image.
  3. 3.Drawing solid lines for virtual images instead of dashed lines.

Analysis and explanation

The position and nature of an image formed by a concave mirror depend on the object's position relative to the focal point (FF) and center of curvature (CC). When u>2fu > 2f, the image is diminished. When u=2fu = 2f, the image is the same size. When u<fu < f, the rays diverge after reflection, and their backward extensions meet to form a virtual, erect, and magnified image behind the mirror.

Interesting facts

Concave mirrors are the only spherical mirrors that can produce both real and virtual images, as well as magnified, diminished, and same-sized images.

Question details

Q39 of 39 questions

Board
CBSE
Class
Class 10
Subject
Science
Year
2024
Section
Section E
Marks
4
Chapter
Chemical Reactions and Equations
Topic
Spherical Mirrors - Concave Mirror
Bloom's level
Applying
Syllabus topic
Light - Reflection and Refraction: Reflection of light by curved surfaces; Images formed by spherical mirrors; Mirror formula

Spotted a mistake or something unclear?

Tell us and we will fix it.

Frequently asked questions

How many marks does this question carry in CBSE Class 10 Science 2024?

This question carries 4 marks in the CBSE Class 10 Science 2024 examination.

Which chapter does this question come from in Science?

This question is from the chapter "Chemical Reactions and Equations" in the CBSE Class 10 Science syllabus.

What topic does this question cover in Science?

This question covers the topic "Spherical Mirrors - Concave Mirror" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2024 paper?

This question appears in Section E in the CBSE Class 10 Science 2024 paper.