Question 248: Ray Optics

Question

An object $$2.4$$ $$m$$ in front of a lens forms a sharp image on a film $$12$$ $$cm$$ behind the lens.  A glass plate $$1$$ $$cm$$ thick, of refractive index $$1.50$$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Accepted Answer

The focal length of the lens
$${1 \over f} = {1 \over \upsilon } - {1 \over u} = {1 \over {12}} + {1 \over {240}}$$
$$ = {{20 + 1} \over {240}} = {{21} \over {240}}$$
$$f = {{240} \over {21}}cm$$
Shift $$ = t\left( {1 - {1 \over \mu }} ight) \Rightarrow 1\left( {1 - {1 \over {3/2}}} ight)$$
$$ = 1 	imes {1 \over 3}$$
Now $$v' = 12 - {1 \over 3} = {{35} \over 3}cm$$
Now the object distancce $$u.$$
$${1 \over u} = {3 \over {35}} - {{21} \over {240}} = {1 \over 5}\left[ {{3 \over 7} - {{21} \over {48}}} ight]$$
$${1 \over u} = {1 \over 5}\left[ {{{48 - 49} \over {7 	imes 16}}} ight]$$
$$u =  - 7 	imes 16 	imes 5 =  - 560cm =  - 5.6\,m$$

Answer

$$7.2$$ $$m$$

Answer

$$24$$ $$m$$

Answer

$$3.2$$ $$m$$

Answer

$$5.6$$ $$m$$

Ray Optics

An object $2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Choose the correct answer: