A ray parallel to the axis enters a plano-convex lens whose curved-surface radius is 10 cm and refractive index is 4/3. The incident ray is 6 cm above the axis as shown. The point where the emerging ray meets axis is at a distance (26y/7) cm from the curved surface. Find y. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A ray parallel to the axis enters a plano-convex lens whose curved-surface radius is 10 cm and refractive index is 4/3. The incident ray is 6 cm above the axis as shown. The point where the emerging ray meets axis is at a distance (26y/7) cm from the curved surface. Find y. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — At the plane entrance, incidence is normal, so the incident ray continues inside the glass at unchanged height h = 6 cm. Step 2 — On curved surface of radius R = 10 cm, the normal makes angle i with axis such that sin i = 6/10 = 3/5. Step 3 — Use refraction from glass (μ = 4/3) to air: sin e = (4/3) sin i = 4/5. Thus cos e = 3/5, while cos i = 4/5. Step 4 — The emerging angle with axis is e−i. Using the intersection geometry and the surface sag, the distance from curved surface to axis…