Question

) An object is placed at a distance of 10 om in
front of a convex whose focal length is 5cm
where
is the image formed draw the ray diagram.​

Answer 1

$\huge\underbrace{\overbrace{\boxed{\boxed{\mathfrak{Answer:}}}}}}$

(a) Refers to the attachment for this answer.

(b)  Focal length(f) of the lens is less than the object distance(u). This means that the Object is kept behind the Focus.

For Convex Mirror, we know that the Characteristics of the Image which is formed when the object is kept between Infinity and Focus are Virtual, Erect, and Diminished at the Point.

(c) Given conditions ⇒

Object Distance(u) = 10 cm. (negative)

Focal length of the lens (f) = 5 cm.

We know, convex mirror always forms the virtual, upright and diminished. Also, Object distance in the convex mirror is always negative where as Image distance and focal length are positive.

Now, Applying the Mirror's Formula,

$\bold{\frac{1}{f}=\frac{1}{u}+\frac{1}{v} }\\\\\bold{\frac{1}{5}=\frac{1}{v}+\frac{1}{-10} }$

⇒  1/5 = (10 - v)/10v

⇒ 10v = 50 - 5v

⇒ 15v = 50

⇒ v = 50/15

∴ v = 10/3  

∴ Image Distance(v) = 3.33 cm.

Hence, the Image is formed on the other side of the Mirror at the distance of 3.33 cm.

Answer 2

Answer:

Object distance,u= -10cm

Object distance,u= -10cmFocal length,f= 5cm

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10 =3/10

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10 =3/10v=10/3

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10 =3/10v=10/3 =3.33cm

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10 =3/10v=10/3 =3.33cmSo, the image is formed 3.33cm behind the mirror.

Object distance,u= -10cmFocal length,f= 5cmBy the mirror's formula,1/v=1/f-1/u =1/5-1/-10 =1/5+1/10 =2+1/10 =3/10v=10/3 =3.33cmSo, the image is formed 3.33cm behind the mirror.