help in physics

Question

1 An object 7.8 cm high is placed 76 cm in front of a converging lens of focal length 23 cm.

Determine the image position and its height.

 

2. A lens has a focal length of + 25 cm and a magnification of 5.00. How far apart are the object

and the image?

 

3 Yellow light of wavelength 617 nm is incident on a double slit where slits are 1.4 mm apart. At

what angle will the fifth order antinodal line appear? 

Answer 1

1)

Object height h_object = 7.8 cm

Object distance d_object = 76 cm

Focal length f= 23 cm

Image distance d_image = ?

Formula for convex mirror is

Solution : Image distance is 32.98 cm and Image height is 3.38 cm.

Answer 2

2)

Focal length f= 25 cm

Magnification M = 5

Distance between the object and the image Δd = |d_image| - |d_object|

The negative values for image distance indicate that the image is an inverted image.

Δd = |d_image| - |d_object| = |-100 | - |20| = 100-20 = 80 cm.

Distance between the object and the image is 80 cm.

Answer 3

3)

Wavelength of the Blue light λ = 617 nm = 617 * 10^-9 m

Distance between two slits d = 1.4 mm = 1.4 * 10^-3 m

Fifth order antinodal line m = 5

We know that Double slit interference Equation : m λ = d sin θ

sin θ =  m λ / d

sin θ =  (5 * 617 * 10^-9) / (1.4 * 10^-3)

sin θ =  2203.57 * 10^-6

θ = 0.126°

Therefore angle of Diffraction is 0.126°.