NCERT Detailed solution | Ray optics 9.2 | class 12th| physics | jee| NEET

Hello students This is NCERT Detailed Question Series for your exam 12th, NEET, JEE In this series you will get the newly detailed solution from ncert. All question will be explained completely This is a genuine effort from SHAKTI Selection Academy to boost your preparation for NEET and JEE Ques A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror. Exp- Theory Explanation: Image Formation by a Convex Mirror A convex mirror is a spherical mirror whose reflecting surface bulges outward. It is also known as a diverging mirror because the reflected rays diverge after reflection. The backward extensions of these rays meet behind the mirror to form a virtual image. In this question, a needle of height 4.5 cm is placed 12 cm away from a convex mirror having a focal length of 15 cm. The objective is to understand the position of the image, its magnification, and how the image changes when the needle is moved farther away from the mirror. 1. Focal Length of a Convex Mirror The focal length of a convex mirror is taken as positive according to the Cartesian sign convention. Its principal focus is virtual and lies behind the mirror. The object is placed in front of the mirror, so the object distance is taken as negative. These sign conventions are important when applying the mirror formula to determine the image position. 2. Location of the Image The mirror formula establishes the relationship between the focal length, object distance and image distance. Using this formula, the position of the image can be determined from the given information. For a convex mirror, the reflected rays diverge and do not actually meet in front of the mirror. However, when these rays are extended backward, they appear to meet behind the mirror. Therefore, the image is always formed behind the mirror, between the pole and the principal focus, for an object placed at a finite distance in front of it. The image is virtual and cannot be obtained on a screen. 3. Magnification and Size of the Image Magnification describes how the image size compares with the object size. For a spherical mirror, it is related to the image distance and object distance. The needle has a height of 4.5 cm. Once the image distance is known, the magnification relation can be used to determine the relative size of the image. For a convex mirror, magnification is positive, indicating that the image is erect. Its magnitude is less than one, which means that the image is diminished, or smaller than the object. Therefore, the image of the needle is virtual, erect and diminished. 4. What Happens When the Needle Is Moved Farther Away? When the needle is moved farther away from a convex mirror, the image moves towards the pole of the mirror. At the same time, the image becomes progressively smaller. This happens because a convex mirror always produces a diminished image, and increasing the object's distance makes the image size decrease further. For an object at a very large distance, the image forms close to the principal focus behind the mirror and becomes highly diminished. 5. Important Concepts to Remember Convex mirror: A diverging mirror that forms a virtual image for a real object. Image location: Behind the mirror, between the pole and the principal focus. Nature of the image: Virtual and erect. Size of the image: Diminished compared with the object. Magnification: Positive and less than one. When the object moves farther away: The image moves towards the pole and becomes smaller. Conclusion: A convex mirror always forms a virtual, erect and diminished image of a real object. As the object moves farther away, its image approaches the principal focus behind the mirror and becomes smaller.