solve the question attache with this question of ray optics of jee advance

To tackle a question from ray optics, especially in the context of JEE Advanced, it’s essential to first understand the fundamental principles involved. Ray optics, or geometrical optics, deals with the behavior of light as rays, focusing on how they interact with various optical elements like lenses and mirrors. Let’s break down a typical problem step-by-step to illustrate how to approach it effectively.

Understanding the Problem

Imagine you have a scenario where light rays are passing through a convex lens. The question might ask you to find the position of the image formed by the lens when an object is placed at a certain distance from it. The key parameters you would typically need include the focal length of the lens and the object distance.

Key Concepts to Remember

• Lens Formula: The relationship between object distance (u), image distance (v), and focal length (f) is given by the lens formula: 1/f = 1/v - 1/u.
• Sign Convention: For lenses, the object distance is taken as negative if the object is on the same side as the incoming light, while the image distance is positive if the image is on the opposite side.
• Magnification: The magnification (m) can be calculated using the formula: m = v/u, which indicates how much larger or smaller the image is compared to the object.

Step-by-Step Solution

Let’s say the problem states that a convex lens has a focal length of 10 cm, and an object is placed 30 cm away from the lens. Here’s how you would solve it:

1. Identify the Given Values

From the problem, we have:

• Focal length (f) = +10 cm (positive for a convex lens)
• Object distance (u) = -30 cm (negative as per the sign convention)

2. Apply the Lens Formula

Using the lens formula, we can rearrange it to find the image distance (v):

1/f = 1/v - 1/u

Substituting the known values:

1/10 = 1/v - 1/(-30)

This simplifies to:

1/10 = 1/v + 1/30

Now, find a common denominator (which is 30v):

3/v = 1/10 + 1/30

Calculating the right side:

1/10 = 3/30, so:

3/v = (3 + 1)/30 = 4/30

Cross-multiplying gives:

3 * 30 = 4v

Thus:

90 = 4v

Solving for v:

v = 90/4 = 22.5 cm

3. Interpret the Result

The positive value of v indicates that the image is formed on the opposite side of the lens from the object, which is typical for a real image produced by a convex lens. Additionally, we can calculate the magnification:

m = v/u = 22.5 / -30 = -0.75

This means the image is inverted and 75% the size of the object.

Final Thoughts

By following these logical steps and applying the relevant formulas, you can effectively solve ray optics problems. Practice with various scenarios will enhance your understanding and speed, which is crucial for competitive exams like JEE Advanced. Always remember to keep the sign conventions in mind, as they play a vital role in determining the nature of the image formed.