Here are some practice questions similar to the one you solved.
Converging (Concave) Mirror
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A concave mirror forms a real image of height 6 cm of an object of height 2 cm placed 24 cm in front of the mirror. Find:
- (a) Image distance
- (b) Focal length
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A concave mirror forms a real image of height 9 cm of an object of height 3 cm placed 30 cm from the mirror. Calculate:
- (a) Image distance
- (b) Focal length
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An object of height 4 cm is placed 18 cm in front of a concave mirror. A real image of height 8 cm is formed. Find:
- (a) Image distance
- (b) Focal length
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A 2 cm tall object is placed 15 cm in front of a concave mirror. The mirror forms a real image of height 4 cm. Find:
- (a) Image distance
- (b) Focal length
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A concave mirror forms a real image of height 10 cm of an object of height 5 cm placed 40 cm from the mirror. Calculate:
- (a) Image distance
- (b) Focal length
Diverging (Convex) Mirror
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A convex mirror forms a virtual image of height 2 cm of an object of height 4 cm placed 24 cm from the mirror. Find:
- (a) Image distance
- (b) Focal length
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A 6 cm tall object is placed 30 cm in front of a convex mirror. The virtual image formed is 3 cm high. Find:
- (a) Image distance
- (b) Focal length
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A convex mirror forms a virtual image of height 1.5 cm of an object of height 3 cm placed 18 cm away. Calculate:
- (a) Image distance
- (b) Focal length
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A 5 cm tall object is placed 40 cm in front of a convex mirror. The virtual image formed is 2.5 cm high. Find:
- (a) Image distance
- (b) Focal length
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A convex mirror forms a virtual image of height 4 cm of an object of height 8 cm placed 36 cm from the mirror. Calculate:
- (a) Image distance
- (b) Focal length
These questions can all be solved using only:
- Magnification:
- Mirror formula:
Here are higher-level CBSE + IIT Foundation numerical problems on mirrors. These require careful use of sign convention, magnification, and the mirror formula.
Level 1
- A 3 cm tall object is placed 18 cm in front of a concave mirror. A real image 4.5 times the size of the object is formed.
- Find the image distance.
- Find the focal length.
Level 2
- A concave mirror produces a real image 24 cm away from the mirror. The image is 3 times the height of the object.
- Find the object distance.
- Find the focal length.
Level 3
- A 2 cm tall object is placed in front of a concave mirror. The image formed is 8 cm tall and lies 48 cm from the mirror.
- Calculate the object distance.
- Find the focal length.
Level 4
- An object is placed 15 cm in front of a convex mirror. The image formed is one-third the size of the object.
- Find the image distance.
- Calculate the focal length.
Level 5
- A convex mirror forms a virtual image 12 cm behind the mirror. The image is one-fourth the size of the object.
- Find the object distance.
- Find the focal length.
Level 6
- A 5 cm tall object is placed in front of a concave mirror. The image formed is 15 cm tall and lies 36 cm in front of the mirror.
- Find the object distance.
- Calculate the focal length.
Level 7
- A concave mirror forms a real image at a distance twice the object distance. The object is 30 cm from the mirror.
- Find the image distance.
- Find the focal length.
- Calculate the magnification.
Level 8
- An object is placed 20 cm in front of a convex mirror. The magnification is +0.4.
- Find the image distance.
- Calculate the focal length.
Level 9
- A concave mirror produces a real image five times the size of the object. The image is formed 75 cm from the mirror.
- Find the object distance.
- Calculate the focal length.
Level 10
- A 4 cm tall object is placed 30 cm from a concave mirror. A real image of height 10 cm is obtained.
- Find the image distance.
- Calculate the focal length.
Level 11 (Mixed Concept)
- A mirror forms an image 0.25 times the height of the object. The image is virtual and 10 cm behind the mirror.
- Identify whether the mirror is concave or convex.
- Find the object distance.
- Calculate the focal length.
Level 12 (Board + Olympiad)
- A 6 cm object is placed in front of a mirror. The image formed is 18 cm high and lies 54 cm from the mirror.
- Determine the type of mirror.
- Find the object distance.
- Find the focal length.
- State whether the image is real or virtual.
These are challenging numericals that test conceptual understanding and are excellent for CBSE Class 10, Olympiad, and IIT Foundation practice.
Here are very challenging mirror numericals involving magnification, sign convention, image nature, focal length, and reasoning. These are harder than typical CBSE questions and suitable for IIT Foundation.
1.
A 4 cm tall object is placed x cm in front of a concave mirror. A real image 5 times the size of the object is formed 48 cm from the mirror.
- Find the value of x.
- Calculate the focal length.
2.
A concave mirror forms a real image 72 cm from the mirror. The image is 4 times the size of the object.
- Find the object distance.
- Find the focal length.
- Determine the position of the object with respect to the centre of curvature.
3.
A 5 cm object produces a real image of height 20 cm. The sum of the object distance and image distance is 100 cm.
- Find the object distance.
- Find the image distance.
- Find the focal length.
4.
An object is placed in front of a convex mirror. The virtual image formed is one-third the size of the object. The distance between the object and image is 48 cm.
- Find the object distance.
- Find the image distance.
- Calculate the focal length.
5.
A concave mirror forms a real image whose height is 6 times the object height. If the image is formed 90 cm from the mirror:
- Find the object distance.
- Find the focal length.
- Calculate the radius of curvature.
6.
An object is placed 15 cm in front of a concave mirror. The image formed is three times the height of the object.
- Find all possible image distances.
- Find all possible focal lengths.
- State the nature of the image in each case.
7.
A mirror forms an image of magnification −2.5. The image distance is 50 cm.
- Find the object distance.
- Identify the type of mirror.
- Calculate the focal length.
8.
A convex mirror has a focal length of 18 cm. An object is placed 54 cm from the mirror.
- Find the image distance.
- Calculate the magnification.
- If the object height is 9 cm, find the image height.
9.
A concave mirror has a focal length of 20 cm. The image formed is three times the size of the object.
- Find all possible object positions.
- Find the corresponding image positions.
- State whether each image is real or virtual.
10.
A 2 cm object is placed in front of a mirror. The image is 8 cm high and is formed 60 cm from the mirror.
- Determine the type of mirror.
- Find the object distance.
- Find the focal length.
- Find the radius of curvature.
11. (Advanced)
A concave mirror forms a real image. The distance between the object and the image is 40 cm, and the image is three times the size of the object.
- Find the object distance.
- Find the image distance.
- Calculate the focal length.
12. (Very Advanced)
An object is placed in front of a mirror. The image is half the size of the object and lies 20 cm behind the mirror.
- Determine the type of mirror.
- Find the object distance.
- Find the focal length.
- Find the radius of curvature.
These problems require combining multiple concepts rather than applying a single formula directly, making them excellent for strong Class 10 and IIT Foundation students.
If you want JEE Foundation/Olympiad level (much tougher than CBSE), here are problems where you must combine the mirror formula, magnification, geometry, and multiple conditions.
Q1. Two Possible Images
A 5 cm tall object is placed 24 cm from a concave mirror. The image formed is twice the size of the object.
Find:
- All possible image distances.
- The focal length in each case.
- Nature of each image.
Q2. Unknown Object Position
A concave mirror forms a real image 64 cm from the mirror. The image is 4 cm taller than the object and is 5 times its size.
Find:
- Object height.
- Object distance.
- Focal length.
Q3. Difference of Distances
The difference between the image distance and object distance for a concave mirror is 36 cm. The magnification is −4.
Find:
- Object distance.
- Image distance.
- Focal length.
Q4. Sum of Distances
The sum of the object distance and image distance is 150 cm. The magnification is −5.
Find:
- Object distance.
- Image distance.
- Focal length.
- Radius of curvature.
Q5. Image Shift
An object is moved 15 cm towards a concave mirror. The image shifts 60 cm.
If the initial object distance is 45 cm, find:
- Initial image distance.
- Final image distance.
- Focal length.
Q6. Moving Object
An object is placed 30 cm in front of a concave mirror. The image is real and magnified.
The object is then moved 10 cm away from the mirror, and the image becomes the same size as the object.
Find the focal length of the mirror.
Q7. Ratio Problem
The ratio of image distance to object distance is 5 : 2.
If the object is 24 cm from a concave mirror, find:
- Image distance.
- Magnification.
- Focal length.
Q8. Height and Distance
A 6 cm object produces an image 15 cm high.
The distance between the object and image is 63 cm.
Find:
- Object distance.
- Image distance.
- Focal length.
Q9. Convex Mirror Challenge
A convex mirror forms an image whose height is 40% of the object height.
The object and image are 42 cm apart.
Find:
- Object distance.
- Image distance.
- Focal length.
Q10. Radius Given
The radius of curvature of a concave mirror is 40 cm.
The image is 3 times the size of the object.
Find:
- All possible object positions.
- Corresponding image positions.
- Nature of each image.
Q11. Reverse Problem
A concave mirror forms a real image at 48 cm.
If the image height is −12 cm and the object height is 3 cm, determine:
- Object distance.
- Magnification.
- Focal length.
- Radius of curvature.
Q12. Olympiad Level
A concave mirror forms a real image. When the object is moved 12 cm towards the mirror, the image size doubles and the image shifts 48 cm.
Find:
- Initial object distance.
- Initial image distance.
- Focal length.
This last problem requires solving simultaneous equations using the mirror formula and magnification, and is at an Olympiad/JEE Foundation level.
