Optics Question 810
Question: A glass sphere, refractive index 1.5 and radius 10 cm, has a spherical cavity of radius 5 cm concentric with it. A narrow beam of parallel light is directed into the sphere. Find the final image and its nature.
Options:
A) 25 cm left of $ S _{4}, $ virtual
B) 25 cm right of $ S _{4}, $ real
C) 15 cm left of $ S _{4}, $ virtual
D) 20 cm right of $ S _{4}, $ virtual
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We will have single surface refractions successively at the four surfaces $ S _{1},S _{2},S _{3} $ and $ S _{4}. $
Do not forget to shift origin to the vertex of respective surface. $ \frac{1.5}{v _{1}}-\frac{1}{\infty }=\frac{( 1.5-1 )}{+10}\text{ }v _{1}=30cm $
First image is object for the refraction at second surface.
For refraction at surface $ S _{2} $ : Light travels from glass to air $ \frac{1}{v _{2}}-\frac{1.5}{( +25 )}=\frac{1-1.5}{( + )5}\text{ }{{v} _{2}}=-25cm $
For refraction at surface $ S _{4} $ : Light travels from air to glass. $ \frac{1.5}{v _{3}}-\frac{1}{( -35 )}=\frac{( 1-1.5 )}{( -5 )}\text{ }{{v} _{3}}=-35/3cm $
For refraction at surface $ S _{4} $ : Light travels from glass to air similarly, $ V _{4}=-25cm $
The final image is virtual, formal at 25 cm to the left of the vertex of surface $ S _{4} $ .
