Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:
1
2
2
3
3
4
Official Solution
Correct Option: (1)
Using the magnification formula for mirrors: For the concave mirror, the object distance is , and the focal length is , where :
For the convex mirror, the object distance is the same, and the focal length is positive: Hence, the ratio of the sizes of the images formed by the convex mirror and the concave mirror is:
Thus, the correct answer is:
02
PYQ 2025
medium
physicsID: jee-main
A concave mirror of focal length in air is dipped in a liquid of refractive index . Its focal length in the liquid will be:
1
2
3
4
Official Solution
Correct Option: (4)
The question asks about the focal length of a concave mirror when it is dipped in a liquid of refractive index . The key concept to understand here is how the properties of a mirror differ from those of a lens regarding the effect of a medium’s refractive index.
Concept:
A mirror forms images by reflecting light rather than refracting it. Thus, the change in the surrounding medium does not affect the focal length of a mirror. The focal length of mirrors remains constant irrespective of the surrounding medium, unlike lenses where the focal length changes when immersed in a different medium.
Explanation:
The focal length of a mirror is determined solely by its geometry, specifically its curvature, according to the formula for a spherical mirror:
Here, is the radius of curvature of the mirror. Since refractive index does not appear in this formula, it indicates that the refractive index of the medium does not affect the focal length of the mirror.
Conclusion:
Therefore, the focal length of a concave mirror remains the same even when it is placed in a medium with a different refractive index.
Thus, the correct answer is .
Hence, the correct choice is:
03
PYQ 2026
medium
physicsID: jee-main
A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.
1
2.5
2
5
3
7.5
4
7
Official Solution
Correct Option: (2)
Step 1: Understanding the Concept:
When an object (rod) lies along the principal axis, we find the positions of the images of its two endpoints using the mirror formula. The length of the image is the distance between these two image points.
Step 2: Key Formula or Approach:
1. Mirror Formula: .
2. Focal length cm (concave mirror).
3. Identify and for the two ends of the rod.
Step 3: Detailed Explanation:
1. Let the rod be placed such that one end is at cm ( , the center of curvature ) and the other end is further away at cm.
2. For End 1 ( cm): Since the object is at , the image is also at ( cm).
3. For End 2 ( cm): . cm.
4. Length of Image cm.
Step 4: Final Answer:
The length of the image is 5 cm.
04
PYQ 2026
medium
physicsID: jee-main
A concave mirror of focal length forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is _____ cm.
Official Solution
Correct Option: (1)
Concept:
Mirror formula: Magnification: Given image is double the size of object: Thus Step 1: {Case 1: Real inverted image} Substitute in mirror formula: Given : Step 2: {Case 2: Virtual erect image} Substitute in mirror formula: Step 3: {Find distance between positions.} Considering mirror sign convention (object distances measured from pole): Thus separation between the two object positions relative to focus geometry becomes
