Question

1. An object 2.25 mm high is 8.5 cm to the left of a convex lens of 5.5-cm focal length.

Answer 1

According to problem ( considering sign convention for convex lens)

height of object = 2.25 mm;

object distance(u)= - 8.5 cm

focal length (f)= 5.5 cm

image distance(v)= ?

Using lens formula

`\begin{gathered} (1)/(f)=\text{ }(1)/(v)-(1)/(u); \\ \therefore(1)/(5.5)=\text{ }(1)/(v)\text{ -}(1)/(-8.5) \\ (1)/(5.5)=(1)/(v)\text{ +}(1)/(8.5); \\ (1)/(v)=(1)/(5.5)-(1)/(8.5)=(3)/(5.5*8.5)=(3)/(46.75) \\ v=(46.75)/(3)=15.58\text{ cm} \end{gathered}`

a) Answer is :- Location of image = 15.58cm

Using magnification formula

`\begin{gathered} Magnification\text{ =}\frac{height\text{ }of\text{ }image}{height\text{ of object}}=(v)/(u) \\ \therefore Magnification=\text{ }(15.58)/(8.5)\text{ =1.83} \\ \therefore\frac{height\text{ }ofimage}{2.25}\text{ =1.83;} \\ \therefore height\text{ of image = 1.83}*2.25=4.12\text{ mm} \end{gathered}`

b) Height of image = 4.12 mm

C) Magnification= 1.83