Refraction Of Light

Lens maker formula,
Case 1 Real image and are positive, is negative, so


Since, magnification for real image,

So. ...(i)
Case 2 Virtual image, as image is formed infront of lens both and are negative, so

or
Given, size of virtual image size of real image
So, ...(ii)
Adding Eqs. (i) and (ii), we get

or
or

Use Snell’s law: Given: - ,
-

Given: Refracted and reflected rays are perpendicular, so angle between them = Let be angle of incidence and be angle of refraction. Then: Using Snell’s Law:

1. The critical angle for a wave is the angle of incidence beyond which total internal reflection occurs. The formula for the critical angle is given by: where is the refractive index of the medium from which the light is coming (air, in this case), and is the refractive index of the medium in which the light is refracted.
2. The refractive index of a medium for different wavelengths (colors of light) varies. For shorter wavelengths (such as violet light), the refractive index is higher, and for longer wavelengths (such as red light), the refractive index is lower.
3. Given that (yellow light) is shorter than (red light), it has a higher refractive index for the same medium.
4. Since is inversely proportional to the refractive index, a higher refractive index results in a smaller critical angle.
5. Therefore, the critical angle for yellow light will be less than the critical angle for red light .

Step 1: Understanding the Apparent Depth Formula When an object is viewed from a rarer medium (air) into a denser medium (water), the apparent depth is given by: where: - is the actual depth, - is the refractive index of the medium (water), - is the apparent depth. Step 2: Substituting the Given Values Given: Using the formula: Step 3: Conclusion Thus, the apparent depth of the object is 75 cm.

The lens makers formula for a lens in a medium is: where is the focal length, is the refractive index of the lens (glass), is the refractive index of the medium, and are the radii of curvature (constant for the lens). - In air ( ): - In liquid ( ): Given the focal length ratio , so , or: Divide the lens maker’s equations: Since , we have: Given : Simplify: Multiply through by 0.5: Solve for : Verify: - In air: . - In liquid: . - Ratio: , so , confirming . Check options: - (1) 1.20: Matches . - (2) 1.30: Gives , ratio , incorrect. - (3) 1.25: Gives , ratio , incorrect. - (4) 1.35: Gives , ratio , incorrect. The error in the original solution ( ) arose from incorrect manipulation; the correct aligns with option (1).