When object is placed at a distance of 40 cm in front of a concave mirror of focal length 20cm?

Text Solution

Solution : Concave mirror <br> u = -40 cm , f= -20 cm , v = ? Nature = ? <br> According to mirror formula <br> ` 1/v + 1/u = 1/f Rightarrow 1/v + 1/(-40) = 1/(-20)` <br> ` Rightarrow 1/v - 1/40 = (-1)/20` <br> ` Rightarrow 1/v = (-1)/20 + 1/40 = ( -2+1)/40 = (-1)/40` <br> v = -40 cm <br> Position : Image is formed 40 cm in front of the concave mirror. <br> Nature : Image is real and inverted . <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/SDS_SCI_X_COD_E01_005_S01.png" width="80%">

Text Solution

real and inverted and of same sizevirtual and erect and of same sizereal and erect and of samee sizevirtual and inverted and of same size

Answer : A

Solution : According to new cartesian sign convention, <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_EGN_24_SP_PS_03_E01_002_S01.png" width="80%"> <br> Object distance u=-40cm <br> Image distance v=? <br> focal length f=-20cm <br> `therefore`From mirror formula <br> `(1)/(v)+(1)/(u)=(1)/(f)` <br> or `(1)/(v)=(1)/(f)-(1)/(u)` <br> or `(1)/(v)=(1)/(-20)-(1)/((-40))=-(1)/(40)` <br> or `v=-40cm` <br> `therefore` The image is on the same side of the object. <br> Now, magniffication <br> `m=-(v)/(u)=-((-40))/((-40))=-1` <br> Hence, the image is real, inverted and of same size.